[{"acknowledgement":"The second author was supported by the priority program SPP2026 of the German Research Foundation (DFG). The fourth author was supported by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG) via RTG 1523/2.","department":[{"_id":"JaMa"}],"title":"Sobolev-type inequalities and eigenvalue growth on graphs with finite measure","oa":1,"publication_status":"published","article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"08","_id":"13177","citation":{"short":"B. Hua, M. Keller, M. Schwarz, M. Wirth, Proceedings of the American Mathematical Society 151 (2023) 3401–3414.","ama":"Hua B, Keller M, Schwarz M, Wirth M. Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. <i>Proceedings of the American Mathematical Society</i>. 2023;151(8):3401-3414. doi:<a href=\"https://doi.org/10.1090/proc/14361\">10.1090/proc/14361</a>","ista":"Hua B, Keller M, Schwarz M, Wirth M. 2023. Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. Proceedings of the American Mathematical Society. 151(8), 3401–3414.","chicago":"Hua, Bobo, Matthias Keller, Michael Schwarz, and Melchior Wirth. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2023. <a href=\"https://doi.org/10.1090/proc/14361\">https://doi.org/10.1090/proc/14361</a>.","apa":"Hua, B., Keller, M., Schwarz, M., &#38; Wirth, M. (2023). Sobolev-type inequalities and eigenvalue growth on graphs with finite measure. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/14361\">https://doi.org/10.1090/proc/14361</a>","ieee":"B. Hua, M. Keller, M. Schwarz, and M. Wirth, “Sobolev-type inequalities and eigenvalue growth on graphs with finite measure,” <i>Proceedings of the American Mathematical Society</i>, vol. 151, no. 8. American Mathematical Society, pp. 3401–3414, 2023.","mla":"Hua, Bobo, et al. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” <i>Proceedings of the American Mathematical Society</i>, vol. 151, no. 8, American Mathematical Society, 2023, pp. 3401–14, doi:<a href=\"https://doi.org/10.1090/proc/14361\">10.1090/proc/14361</a>."},"intvolume":"       151","day":"01","status":"public","abstract":[{"lang":"eng","text":"In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities and that the total measure is finite. In this sense, the associated operators on these graphs display similarities to elliptic operators on bounded domains in the continuum. Specifically, we prove lower bounds on the eigenvalue growth and show by examples that corresponding upper bounds cannot be established."}],"publication":"Proceedings of the American Mathematical Society","issue":"8","author":[{"full_name":"Hua, Bobo","first_name":"Bobo","last_name":"Hua"},{"first_name":"Matthias","full_name":"Keller, Matthias","last_name":"Keller"},{"first_name":"Michael","full_name":"Schwarz, Michael","last_name":"Schwarz"},{"full_name":"Wirth, Melchior","first_name":"Melchior","last_name":"Wirth","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241"}],"oa_version":"Preprint","external_id":{"arxiv":["1804.08353"],"isi":["000988204400001"]},"date_published":"2023-08-01T00:00:00Z","language":[{"iso":"eng"}],"arxiv":1,"type":"journal_article","doi":"10.1090/proc/14361","publisher":"American Mathematical Society","publication_identifier":{"issn":["0002-9939"],"eissn":["1088-6826"]},"scopus_import":"1","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.1804.08353"}],"article_processing_charge":"No","volume":151,"isi":1,"page":"3401-3414","quality_controlled":"1","year":"2023","date_created":"2023-07-02T22:00:43Z","date_updated":"2023-11-14T13:07:09Z"},{"department":[{"_id":"JaMa"}],"acknowledgement":"The authors are grateful to Martijn Caspers for helpful comments on a preliminary version of this manuscript. M. V. was supported by the NWO Vidi grant VI.Vidi.192.018 ‘Non-commutative harmonic analysis and rigidity of operator algebras’. M. W. was funded by the Austrian Science Fund (FWF) under the Esprit Programme [ESP 156]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission. Open access funding provided by Austrian Science Fund (FWF).","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"13319","month":"10","title":"Derivations and KMS-symmetric quantum Markov semigroups","oa":1,"publication_status":"published","article_type":"original","day":"01","has_accepted_license":"1","intvolume":"       403","citation":{"short":"M. Vernooij, M. Wirth, Communications in Mathematical Physics 403 (2023) 381–416.","ama":"Vernooij M, Wirth M. Derivations and KMS-symmetric quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. 2023;403:381-416. doi:<a href=\"https://doi.org/10.1007/s00220-023-04795-6\">10.1007/s00220-023-04795-6</a>","apa":"Vernooij, M., &#38; Wirth, M. (2023). Derivations and KMS-symmetric quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04795-6\">https://doi.org/10.1007/s00220-023-04795-6</a>","chicago":"Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04795-6\">https://doi.org/10.1007/s00220-023-04795-6</a>.","ista":"Vernooij M, Wirth M. 2023. Derivations and KMS-symmetric quantum Markov semigroups. Communications in Mathematical Physics. 403, 381–416.","ieee":"M. Vernooij and M. Wirth, “Derivations and KMS-symmetric quantum Markov semigroups,” <i>Communications in Mathematical Physics</i>, vol. 403. Springer Nature, pp. 381–416, 2023.","mla":"Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>, vol. 403, Springer Nature, 2023, pp. 381–416, doi:<a href=\"https://doi.org/10.1007/s00220-023-04795-6\">10.1007/s00220-023-04795-6</a>."},"status":"public","abstract":[{"lang":"eng","text":"We prove that the generator of the L2 implementation of a KMS-symmetric quantum Markov semigroup can be expressed as the square of a derivation with values in a Hilbert bimodule, extending earlier results by Cipriani and Sauvageot for tracially symmetric semigroups and the second-named author for GNS-symmetric semigroups. This result hinges on the introduction of a new completely positive map on the algebra of bounded operators on the GNS Hilbert space. This transformation maps symmetric Markov operators to symmetric Markov operators and is essential to obtain the required inner product on the Hilbert bimodule."}],"oa_version":"Published Version","external_id":{"arxiv":["2303.15949"],"isi":["001033655400002"]},"date_published":"2023-10-01T00:00:00Z","publication":"Communications in Mathematical Physics","ddc":["510"],"author":[{"first_name":"Matthijs","full_name":"Vernooij, Matthijs","last_name":"Vernooij"},{"last_name":"Wirth","full_name":"Wirth, Melchior","first_name":"Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241"}],"doi":"10.1007/s00220-023-04795-6","publisher":"Springer Nature","language":[{"iso":"eng"}],"arxiv":1,"file_date_updated":"2024-01-30T12:15:11Z","type":"journal_article","article_processing_charge":"Yes (via OA deal)","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"scopus_import":"1","quality_controlled":"1","page":"381-416","year":"2023","date_created":"2023-07-30T22:01:03Z","date_updated":"2024-01-30T12:16:32Z","project":[{"_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","name":"Gradient flow techniques for quantum Markov semigroups","grant_number":"ESP156_N"}],"volume":403,"file":[{"checksum":"cca204e81891270216a0c84eb8bcd398","relation":"main_file","creator":"dernst","file_size":481209,"file_name":"2023_CommMathPhysics_Vernooij.pdf","date_updated":"2024-01-30T12:15:11Z","access_level":"open_access","success":1,"date_created":"2024-01-30T12:15:11Z","content_type":"application/pdf","file_id":"14905"}],"isi":1},{"date_published":"2023-03-01T00:00:00Z","oa_version":"Published Version","external_id":{"arxiv":["2105.08303"],"isi":["000837499800002"]},"author":[{"orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","full_name":"Wirth, Melchior","first_name":"Melchior","last_name":"Wirth"},{"first_name":"Haonan","full_name":"Zhang, Haonan","last_name":"Zhang","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425"}],"ddc":["510"],"publication":"Annales Henri Poincare","publisher":"Springer Nature","doi":"10.1007/s00023-022-01220-x","type":"journal_article","file_date_updated":"2023-08-14T11:38:28Z","arxiv":1,"language":[{"iso":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"Yes (via OA deal)","scopus_import":"1","publication_identifier":{"issn":["1424-0637"]},"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"Curvature-dimension in noncommutative analysis","grant_number":"M03337","_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6"},{"grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"}],"date_updated":"2023-08-14T11:39:28Z","year":"2023","date_created":"2022-09-11T22:01:57Z","quality_controlled":"1","page":"717-750","isi":1,"file":[{"date_updated":"2023-08-14T11:38:28Z","access_level":"open_access","success":1,"date_created":"2023-08-14T11:38:28Z","content_type":"application/pdf","file_id":"14051","file_name":"2023_AnnalesHenriPoincare_Wirth.pdf","creator":"dernst","file_size":554871,"checksum":"8c7b185eba5ccd92ef55c120f654222c","relation":"main_file"}],"volume":24,"acknowledgement":"H.Z. is supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411 and the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. M.W. acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117) and from the Austrian Science Fund (FWF) through grant number F65. Both authors would like to thank Jan Maas for fruitful discussions and helpful comments. Open access funding provided by Austrian Science Fund (FWF).","department":[{"_id":"JaMa"}],"month":"03","_id":"12087","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_type":"original","publication_status":"published","title":"Curvature-dimension conditions for symmetric quantum Markov semigroups","oa":1,"has_accepted_license":"1","day":"01","intvolume":"        24","citation":{"chicago":"Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” <i>Annales Henri Poincare</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00023-022-01220-x\">https://doi.org/10.1007/s00023-022-01220-x</a>.","apa":"Wirth, M., &#38; Zhang, H. (2023). Curvature-dimension conditions for symmetric quantum Markov semigroups. <i>Annales Henri Poincare</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-022-01220-x\">https://doi.org/10.1007/s00023-022-01220-x</a>","ista":"Wirth M, Zhang H. 2023. Curvature-dimension conditions for symmetric quantum Markov semigroups. Annales Henri Poincare. 24, 717–750.","ieee":"M. Wirth and H. Zhang, “Curvature-dimension conditions for symmetric quantum Markov semigroups,” <i>Annales Henri Poincare</i>, vol. 24. Springer Nature, pp. 717–750, 2023.","mla":"Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric Quantum Markov Semigroups.” <i>Annales Henri Poincare</i>, vol. 24, Springer Nature, 2023, pp. 717–50, doi:<a href=\"https://doi.org/10.1007/s00023-022-01220-x\">10.1007/s00023-022-01220-x</a>.","short":"M. Wirth, H. Zhang, Annales Henri Poincare 24 (2023) 717–750.","ama":"Wirth M, Zhang H. Curvature-dimension conditions for symmetric quantum Markov semigroups. <i>Annales Henri Poincare</i>. 2023;24:717-750. doi:<a href=\"https://doi.org/10.1007/s00023-022-01220-x\">10.1007/s00023-022-01220-x</a>"},"ec_funded":1,"abstract":[{"lang":"eng","text":"Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet–Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension conditions, including Schur multipliers over matrix algebras, Herz–Schur multipliers over group algebras and generalized depolarizing semigroups."}],"status":"public"},{"doi":"10.1007/s00028-022-00859-7","publisher":"Springer Nature","language":[{"iso":"eng"}],"file_date_updated":"2023-01-20T10:45:06Z","type":"journal_article","oa_version":"Published Version","external_id":{"isi":["000906214600004"]},"date_published":"2023-01-01T00:00:00Z","issue":"1","publication":"Journal of Evolution Equations","ddc":["510"],"author":[{"id":"ECEBF480-9E4F-11EA-B557-B0823DDC885E","orcid":"0000-0002-9881-6870","last_name":"Dello Schiavo","first_name":"Lorenzo","full_name":"Dello Schiavo, Lorenzo"},{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","first_name":"Melchior","full_name":"Wirth, Melchior","last_name":"Wirth"}],"quality_controlled":"1","year":"2023","date_created":"2023-01-08T23:00:53Z","date_updated":"2023-06-28T11:54:35Z","project":[{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"},{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"},{"name":"Configuration Spaces over Non-Smooth Spaces","grant_number":"E208","_id":"34dbf174-11ca-11ed-8bc3-afe9d43d4b9c"},{"_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","name":"Gradient flow techniques for quantum Markov semigroups","grant_number":"ESP156_N"}],"volume":23,"file":[{"file_name":"2023_JourEvolutionEquations_DelloSchiavo.pdf","file_id":"12325","content_type":"application/pdf","date_created":"2023-01-20T10:45:06Z","access_level":"open_access","success":1,"date_updated":"2023-01-20T10:45:06Z","relation":"main_file","checksum":"1f34f3e2cb521033de6154f274ea3a4e","file_size":422612,"creator":"dernst"}],"isi":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"Yes (via OA deal)","publication_identifier":{"eissn":["1424-3202"],"issn":["1424-3199"]},"scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"12104","month":"01","oa":1,"title":"Ergodic decompositions of Dirichlet forms under order isomorphisms","publication_status":"published","article_type":"original","department":[{"_id":"JaMa"}],"acknowledgement":"Research supported by the Austrian Science Fund (FWF) grant F65 at the Institute of Science and Technology Austria and by the European Research Council (ERC) (Grant agreement No. 716117 awarded to Prof. Dr. Jan Maas). L.D.S. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 208). M.W. gratefully acknowledges funding of his current position by the Austrian Science Fund (FWF) through the ESPRIT Programme (Grant No. 156).","ec_funded":1,"article_number":"9","status":"public","abstract":[{"text":"We study ergodic decompositions of Dirichlet spaces under intertwining via unitary order isomorphisms. We show that the ergodic decomposition of a quasi-regular Dirichlet space is unique up to a unique isomorphism of the indexing space. Furthermore, every unitary order isomorphism intertwining two quasi-regular Dirichlet spaces is decomposable over their ergodic decompositions up to conjugation via an isomorphism of the corresponding indexing spaces.","lang":"eng"}],"day":"01","has_accepted_license":"1","citation":{"ama":"Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order isomorphisms. <i>Journal of Evolution Equations</i>. 2023;23(1). doi:<a href=\"https://doi.org/10.1007/s00028-022-00859-7\">10.1007/s00028-022-00859-7</a>","short":"L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023).","mla":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” <i>Journal of Evolution Equations</i>, vol. 23, no. 1, 9, Springer Nature, 2023, doi:<a href=\"https://doi.org/10.1007/s00028-022-00859-7\">10.1007/s00028-022-00859-7</a>.","ieee":"L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms under order isomorphisms,” <i>Journal of Evolution Equations</i>, vol. 23, no. 1. Springer Nature, 2023.","ista":"Dello Schiavo L, Wirth M. 2023. Ergodic decompositions of Dirichlet forms under order isomorphisms. Journal of Evolution Equations. 23(1), 9.","chicago":"Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet Forms under Order Isomorphisms.” <i>Journal of Evolution Equations</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00028-022-00859-7\">https://doi.org/10.1007/s00028-022-00859-7</a>.","apa":"Dello Schiavo, L., &#38; Wirth, M. (2023). Ergodic decompositions of Dirichlet forms under order isomorphisms. <i>Journal of Evolution Equations</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00028-022-00859-7\">https://doi.org/10.1007/s00028-022-00859-7</a>"},"intvolume":"        23"},{"date_created":"2022-04-24T22:01:43Z","year":"2022","quality_controlled":"1","project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems"},{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"date_updated":"2023-08-03T06:37:49Z","isi":1,"file":[{"creator":"dernst","file_size":362119,"checksum":"f3e0b00884b7dde31347a3756788b473","relation":"main_file","access_level":"open_access","success":1,"date_updated":"2022-04-29T11:24:23Z","content_type":"application/pdf","date_created":"2022-04-29T11:24:23Z","file_id":"11338","file_name":"2022_JourStatisticalPhysics_Wirth.pdf"}],"volume":187,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"Yes (via OA deal)","publication_identifier":{"eissn":["15729613"],"issn":["00224715"]},"scopus_import":"1","doi":"10.1007/s10955-022-02911-9","publisher":"Springer Nature","language":[{"iso":"eng"}],"type":"journal_article","file_date_updated":"2022-04-29T11:24:23Z","external_id":{"isi":["000780305000001"]},"oa_version":"Published Version","date_published":"2022-04-08T00:00:00Z","publication":"Journal of Statistical Physics","issue":"2","author":[{"full_name":"Wirth, Melchior","first_name":"Melchior","last_name":"Wirth","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241"}],"ddc":["510","530"],"ec_funded":1,"status":"public","article_number":"19","abstract":[{"lang":"eng","text":"In this article we study the noncommutative transport distance introduced by Carlen and Maas and its entropic regularization defined by Becker and Li. We prove a duality formula that can be understood as a quantum version of the dual Benamou–Brenier formulation of the Wasserstein distance in terms of subsolutions of a Hamilton–Jacobi–Bellmann equation."}],"day":"08","has_accepted_license":"1","intvolume":"       187","citation":{"short":"M. Wirth, Journal of Statistical Physics 187 (2022).","ama":"Wirth M. A dual formula for the noncommutative transport distance. <i>Journal of Statistical Physics</i>. 2022;187(2). doi:<a href=\"https://doi.org/10.1007/s10955-022-02911-9\">10.1007/s10955-022-02911-9</a>","ista":"Wirth M. 2022. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 187(2), 19.","chicago":"Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” <i>Journal of Statistical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10955-022-02911-9\">https://doi.org/10.1007/s10955-022-02911-9</a>.","apa":"Wirth, M. (2022). A dual formula for the noncommutative transport distance. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-022-02911-9\">https://doi.org/10.1007/s10955-022-02911-9</a>","mla":"Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” <i>Journal of Statistical Physics</i>, vol. 187, no. 2, 19, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s10955-022-02911-9\">10.1007/s10955-022-02911-9</a>.","ieee":"M. Wirth, “A dual formula for the noncommutative transport distance,” <i>Journal of Statistical Physics</i>, vol. 187, no. 2. Springer Nature, 2022."},"_id":"11330","month":"04","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_status":"published","oa":1,"title":"A dual formula for the noncommutative transport distance","article_type":"original","acknowledgement":"The author wants to thank Jan Maas for helpful comments. He also acknowledges financial support from the Austrian Science Fund (FWF) through Grant Number F65 and from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (Grant Agreement No. 716117).\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","department":[{"_id":"JaMa"}]},{"language":[{"iso":"eng"}],"file_date_updated":"2022-08-18T08:02:34Z","type":"journal_article","doi":"10.1007/s43036-022-00199-w","publisher":"Springer Nature","issue":"3","publication":"Advances in Operator Theory","ddc":["510"],"author":[{"last_name":"Wirth","full_name":"Wirth, Melchior","first_name":"Melchior","orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"}],"oa_version":"Published Version","date_published":"2022-07-01T00:00:00Z","volume":7,"file":[{"relation":"main_file","checksum":"913474844a1b38264fb710746d5e2e98","file_size":389060,"creator":"dernst","file_name":"2022_AdvancesOperatorTheory_Wirth.pdf","date_created":"2022-08-18T08:02:34Z","content_type":"application/pdf","file_id":"11921","date_updated":"2022-08-18T08:02:34Z","success":1,"access_level":"open_access"}],"quality_controlled":"1","date_created":"2022-08-18T07:22:24Z","year":"2022","date_updated":"2023-02-21T10:08:07Z","publication_identifier":{"eissn":["2538-225X"]},"scopus_import":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"Yes (via OA deal)","title":"Kac regularity and domination of quadratic forms","oa":1,"publication_status":"published","article_type":"original","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"11916","month":"07","acknowledgement":"The author was supported by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes) and by the German Research Foundation (DFG) via RTG 1523/2. The author would like to thank Daniel Lenz for his support and encouragement during the author’s ongoing graduate studies and him as well as Marcel Schmidt for fruitful discussions on domination of quadratic forms. He wants to thank Batu Güneysu and Peter Stollmann for valuable comments on a preliminary version of this article. He would also like to thank the organizers of the conference Analysis and Geometry on Graphs and Manifolds in Potsdam, where the initial motivation of this article was conceived, and the organizers of the intense activity period Metric Measure Spaces and Ricci Curvature at MPIM in Bonn, where this work was finished.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","department":[{"_id":"JaMa"}],"article_number":"38","status":"public","abstract":[{"lang":"eng","text":"A domain is called Kac regular for a quadratic form on L2 if every functions vanishing almost everywhere outside the domain can be approximated in form norm by functions with compact support in the domain. It is shown that this notion is stable under domination of quadratic forms. As applications measure perturbations of quasi-regular Dirichlet forms, Cheeger energies on metric measure spaces and Schrödinger operators on manifolds are studied. Along the way a characterization of the Sobolev space with Dirichlet boundary conditions on domains in infinitesimally Riemannian metric measure spaces is obtained."}],"keyword":["Algebra and Number Theory","Analysis"],"citation":{"ieee":"M. Wirth, “Kac regularity and domination of quadratic forms,” <i>Advances in Operator Theory</i>, vol. 7, no. 3. Springer Nature, 2022.","mla":"Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” <i>Advances in Operator Theory</i>, vol. 7, no. 3, 38, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s43036-022-00199-w\">10.1007/s43036-022-00199-w</a>.","ista":"Wirth M. 2022. Kac regularity and domination of quadratic forms. Advances in Operator Theory. 7(3), 38.","chicago":"Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” <i>Advances in Operator Theory</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s43036-022-00199-w\">https://doi.org/10.1007/s43036-022-00199-w</a>.","apa":"Wirth, M. (2022). Kac regularity and domination of quadratic forms. <i>Advances in Operator Theory</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s43036-022-00199-w\">https://doi.org/10.1007/s43036-022-00199-w</a>","ama":"Wirth M. Kac regularity and domination of quadratic forms. <i>Advances in Operator Theory</i>. 2022;7(3). doi:<a href=\"https://doi.org/10.1007/s43036-022-00199-w\">10.1007/s43036-022-00199-w</a>","short":"M. Wirth, Advances in Operator Theory 7 (2022)."},"intvolume":"         7","day":"01","has_accepted_license":"1"},{"date_published":"2021-08-01T00:00:00Z","external_id":{"arxiv":["1912.03670"],"isi":["000721363700003"]},"oa_version":"Published Version","author":[{"first_name":"Daniel","full_name":"Lenz, Daniel","last_name":"Lenz"},{"last_name":"Weinmann","full_name":"Weinmann, Timon","first_name":"Timon"},{"last_name":"Wirth","first_name":"Melchior","full_name":"Wirth, Melchior","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241"}],"publication":"Proceedings of the Edinburgh Mathematical Society","issue":"3","publisher":"Cambridge University Press","doi":"10.1017/S0013091521000080","type":"journal_article","arxiv":1,"language":[{"iso":"eng"}],"article_processing_charge":"No","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1017/S0013091521000080"}],"publication_identifier":{"issn":["0013-0915"],"eissn":["1464-3839"]},"date_updated":"2023-08-17T07:12:05Z","quality_controlled":"1","page":"443-447","date_created":"2021-07-04T22:01:24Z","year":"2021","volume":64,"isi":1,"department":[{"_id":"JaMa"}],"acknowledgement":"M. W. gratefully acknowledges financial support by the German Academic Scholarship Foundation (Studienstiftung des deutschen Volkes). T.W. thanks PAO Gazprom Neft, the Euler International Mathematical Institute in Saint Petersburg and ORISA GmbH for their financial support in the form of scholarships during his Master's and Bachelor's studies respectively. The authors want to thank Mark Malamud for pointing out the reference [1] to them. This work was supported by the Ministry of Science and Higher Education of the Russian Federation, agreement No 075-15-2019-1619.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"08","_id":"9627","article_type":"original","title":"Self-adjoint extensions of bipartite Hamiltonians","oa":1,"publication_status":"published","day":"01","intvolume":"        64","citation":{"mla":"Lenz, Daniel, et al. “Self-Adjoint Extensions of Bipartite Hamiltonians.” <i>Proceedings of the Edinburgh Mathematical Society</i>, vol. 64, no. 3, Cambridge University Press, 2021, pp. 443–47, doi:<a href=\"https://doi.org/10.1017/S0013091521000080\">10.1017/S0013091521000080</a>.","ieee":"D. Lenz, T. Weinmann, and M. Wirth, “Self-adjoint extensions of bipartite Hamiltonians,” <i>Proceedings of the Edinburgh Mathematical Society</i>, vol. 64, no. 3. Cambridge University Press, pp. 443–447, 2021.","chicago":"Lenz, Daniel, Timon Weinmann, and Melchior Wirth. “Self-Adjoint Extensions of Bipartite Hamiltonians.” <i>Proceedings of the Edinburgh Mathematical Society</i>. Cambridge University Press, 2021. <a href=\"https://doi.org/10.1017/S0013091521000080\">https://doi.org/10.1017/S0013091521000080</a>.","apa":"Lenz, D., Weinmann, T., &#38; Wirth, M. (2021). Self-adjoint extensions of bipartite Hamiltonians. <i>Proceedings of the Edinburgh Mathematical Society</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/S0013091521000080\">https://doi.org/10.1017/S0013091521000080</a>","ista":"Lenz D, Weinmann T, Wirth M. 2021. Self-adjoint extensions of bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society. 64(3), 443–447.","ama":"Lenz D, Weinmann T, Wirth M. Self-adjoint extensions of bipartite Hamiltonians. <i>Proceedings of the Edinburgh Mathematical Society</i>. 2021;64(3):443-447. doi:<a href=\"https://doi.org/10.1017/S0013091521000080\">10.1017/S0013091521000080</a>","short":"D. Lenz, T. Weinmann, M. Wirth, Proceedings of the Edinburgh Mathematical Society 64 (2021) 443–447."},"abstract":[{"lang":"eng","text":"We compute the deficiency spaces of operators of the form 𝐻𝐴⊗̂ 𝐼+𝐼⊗̂ 𝐻𝐵, for symmetric 𝐻𝐴 and self-adjoint 𝐻𝐵. This enables us to construct self-adjoint extensions (if they exist) by means of von Neumann's theory. The structure of the deficiency spaces for this case was asserted already in Ibort et al. [Boundary dynamics driven entanglement, J. Phys. A: Math. Theor. 47(38) (2014) 385301], but only proven under the restriction of 𝐻𝐵 having discrete, non-degenerate spectrum."}],"status":"public"},{"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"intvolume":"       387","citation":{"apa":"Wirth, M., &#38; Zhang, H. (2021). Complete gradient estimates of quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-021-04199-4\">https://doi.org/10.1007/s00220-021-04199-4</a>","chicago":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00220-021-04199-4\">https://doi.org/10.1007/s00220-021-04199-4</a>.","ista":"Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 387, 761–791.","ieee":"M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,” <i>Communications in Mathematical Physics</i>, vol. 387. Springer Nature, pp. 761–791, 2021.","mla":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>, vol. 387, Springer Nature, 2021, pp. 761–791, doi:<a href=\"https://doi.org/10.1007/s00220-021-04199-4\">10.1007/s00220-021-04199-4</a>.","short":"M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791.","ama":"Wirth M, Zhang H. Complete gradient estimates of quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. 2021;387:761–791. doi:<a href=\"https://doi.org/10.1007/s00220-021-04199-4\">10.1007/s00220-021-04199-4</a>"},"day":"30","has_accepted_license":"1","status":"public","abstract":[{"text":"In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors.","lang":"eng"}],"ec_funded":1,"department":[{"_id":"JaMa"}],"acknowledgement":"Both authors would like to thank Jan Maas for fruitful discussions and helpful comments.","title":"Complete gradient estimates of quantum Markov semigroups","oa":1,"publication_status":"published","article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9973","month":"08","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"scopus_import":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"Yes (via OA deal)","volume":387,"isi":1,"file":[{"file_name":"2021_CommunMathPhys_Wirth.pdf","content_type":"application/pdf","date_created":"2021-09-08T07:34:24Z","file_id":"9990","date_updated":"2021-09-08T09:46:34Z","access_level":"open_access","relation":"main_file","checksum":"8a602f916b1c2b0dc1159708b7cb204b","file_size":505971,"creator":"cchlebak"}],"page":"761–791","quality_controlled":"1","year":"2021","date_created":"2021-08-30T10:07:44Z","date_updated":"2023-08-11T11:09:07Z","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"publication":"Communications in Mathematical Physics","ddc":["621"],"author":[{"id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","orcid":"0000-0002-0519-4241","last_name":"Wirth","full_name":"Wirth, Melchior","first_name":"Melchior"},{"last_name":"Zhang","full_name":"Zhang, Haonan","first_name":"Haonan","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425"}],"external_id":{"arxiv":["2007.13506"],"isi":["000691214200001"]},"oa_version":"Published Version","date_published":"2021-08-30T00:00:00Z","arxiv":1,"language":[{"iso":"eng"}],"file_date_updated":"2021-09-08T09:46:34Z","type":"journal_article","doi":"10.1007/s00220-021-04199-4","publisher":"Springer Nature"}]