---
_id: '13177'
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.
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.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Bobo
full_name: Hua, Bobo
last_name: Hua
- first_name: Matthias
full_name: Keller, Matthias
last_name: Keller
- first_name: Michael
full_name: Schwarz, Michael
last_name: Schwarz
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Hua B, Keller M, Schwarz M, Wirth M. Sobolev-type inequalities and eigenvalue
growth on graphs with finite measure. Proceedings of the American Mathematical
Society. 2023;151(8):3401-3414. doi:10.1090/proc/14361
apa: 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. American Mathematical Society. https://doi.org/10.1090/proc/14361
chicago: Hua, Bobo, Matthias Keller, Michael Schwarz, and Melchior Wirth. “Sobolev-Type
Inequalities and Eigenvalue Growth on Graphs with Finite Measure.” Proceedings
of the American Mathematical Society. American Mathematical Society, 2023.
https://doi.org/10.1090/proc/14361.
ieee: B. Hua, M. Keller, M. Schwarz, and M. Wirth, “Sobolev-type inequalities and
eigenvalue growth on graphs with finite measure,” Proceedings of the American
Mathematical Society, vol. 151, no. 8. American Mathematical Society, pp.
3401–3414, 2023.
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.
mla: Hua, Bobo, et al. “Sobolev-Type Inequalities and Eigenvalue Growth on Graphs
with Finite Measure.” Proceedings of the American Mathematical Society,
vol. 151, no. 8, American Mathematical Society, 2023, pp. 3401–14, doi:10.1090/proc/14361.
short: B. Hua, M. Keller, M. Schwarz, M. Wirth, Proceedings of the American Mathematical
Society 151 (2023) 3401–3414.
date_created: 2023-07-02T22:00:43Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2023-11-14T13:07:09Z
day: '01'
department:
- _id: JaMa
doi: 10.1090/proc/14361
external_id:
arxiv:
- '1804.08353'
isi:
- '000988204400001'
intvolume: ' 151'
isi: 1
issue: '8'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.1804.08353'
month: '08'
oa: 1
oa_version: Preprint
page: 3401-3414
publication: Proceedings of the American Mathematical Society
publication_identifier:
eissn:
- 1088-6826
issn:
- 0002-9939
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sobolev-type inequalities and eigenvalue growth on graphs with finite measure
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 151
year: '2023'
...
---
_id: '13319'
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.
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).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Matthijs
full_name: Vernooij, Matthijs
last_name: Vernooij
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Vernooij M, Wirth M. Derivations and KMS-symmetric quantum Markov semigroups.
Communications in Mathematical Physics. 2023;403:381-416. doi:10.1007/s00220-023-04795-6
apa: Vernooij, M., & Wirth, M. (2023). Derivations and KMS-symmetric quantum
Markov semigroups. Communications in Mathematical Physics. Springer Nature.
https://doi.org/10.1007/s00220-023-04795-6
chicago: Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric
Quantum Markov Semigroups.” Communications in Mathematical Physics. Springer
Nature, 2023. https://doi.org/10.1007/s00220-023-04795-6.
ieee: M. Vernooij and M. Wirth, “Derivations and KMS-symmetric quantum Markov semigroups,”
Communications in Mathematical Physics, vol. 403. Springer Nature, pp.
381–416, 2023.
ista: Vernooij M, Wirth M. 2023. Derivations and KMS-symmetric quantum Markov semigroups.
Communications in Mathematical Physics. 403, 381–416.
mla: Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum
Markov Semigroups.” Communications in Mathematical Physics, vol. 403, Springer
Nature, 2023, pp. 381–416, doi:10.1007/s00220-023-04795-6.
short: M. Vernooij, M. Wirth, Communications in Mathematical Physics 403 (2023)
381–416.
date_created: 2023-07-30T22:01:03Z
date_published: 2023-10-01T00:00:00Z
date_updated: 2024-01-30T12:16:32Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00220-023-04795-6
external_id:
arxiv:
- '2303.15949'
isi:
- '001033655400002'
file:
- access_level: open_access
checksum: cca204e81891270216a0c84eb8bcd398
content_type: application/pdf
creator: dernst
date_created: 2024-01-30T12:15:11Z
date_updated: 2024-01-30T12:15:11Z
file_id: '14905'
file_name: 2023_CommMathPhysics_Vernooij.pdf
file_size: 481209
relation: main_file
success: 1
file_date_updated: 2024-01-30T12:15:11Z
has_accepted_license: '1'
intvolume: ' 403'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 381-416
project:
- _id: 34c6ea2d-11ca-11ed-8bc3-c04f3c502833
grant_number: ESP156_N
name: Gradient flow techniques for quantum Markov semigroups
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Derivations and KMS-symmetric quantum Markov semigroups
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 403
year: '2023'
...
---
_id: '12087'
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.
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).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
- first_name: Haonan
full_name: Zhang, Haonan
id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
last_name: Zhang
citation:
ama: Wirth M, Zhang H. Curvature-dimension conditions for symmetric quantum Markov
semigroups. Annales Henri Poincare. 2023;24:717-750. doi:10.1007/s00023-022-01220-x
apa: Wirth, M., & Zhang, H. (2023). Curvature-dimension conditions for symmetric
quantum Markov semigroups. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-022-01220-x
chicago: Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for
Symmetric Quantum Markov Semigroups.” Annales Henri Poincare. Springer
Nature, 2023. https://doi.org/10.1007/s00023-022-01220-x.
ieee: M. Wirth and H. Zhang, “Curvature-dimension conditions for symmetric quantum
Markov semigroups,” Annales Henri Poincare, vol. 24. Springer Nature, pp.
717–750, 2023.
ista: Wirth M, Zhang H. 2023. Curvature-dimension conditions for symmetric quantum
Markov semigroups. Annales Henri Poincare. 24, 717–750.
mla: Wirth, Melchior, and Haonan Zhang. “Curvature-Dimension Conditions for Symmetric
Quantum Markov Semigroups.” Annales Henri Poincare, vol. 24, Springer Nature,
2023, pp. 717–50, doi:10.1007/s00023-022-01220-x.
short: M. Wirth, H. Zhang, Annales Henri Poincare 24 (2023) 717–750.
date_created: 2022-09-11T22:01:57Z
date_published: 2023-03-01T00:00:00Z
date_updated: 2023-08-14T11:39:28Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00023-022-01220-x
ec_funded: 1
external_id:
arxiv:
- '2105.08303'
isi:
- '000837499800002'
file:
- access_level: open_access
checksum: 8c7b185eba5ccd92ef55c120f654222c
content_type: application/pdf
creator: dernst
date_created: 2023-08-14T11:38:28Z
date_updated: 2023-08-14T11:38:28Z
file_id: '14051'
file_name: 2023_AnnalesHenriPoincare_Wirth.pdf
file_size: 554871
relation: main_file
success: 1
file_date_updated: 2023-08-14T11:38:28Z
has_accepted_license: '1'
intvolume: ' 24'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 717-750
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: eb958bca-77a9-11ec-83b8-c565cb50d8d6
grant_number: M03337
name: Curvature-dimension in noncommutative analysis
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Annales Henri Poincare
publication_identifier:
issn:
- 1424-0637
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Curvature-dimension conditions for symmetric quantum Markov semigroups
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 24
year: '2023'
...
---
_id: '12104'
abstract:
- lang: eng
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.
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).
article_number: '9'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Lorenzo
full_name: Dello Schiavo, Lorenzo
id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
last_name: Dello Schiavo
orcid: 0000-0002-9881-6870
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Dello Schiavo L, Wirth M. Ergodic decompositions of Dirichlet forms under order
isomorphisms. Journal of Evolution Equations. 2023;23(1). doi:10.1007/s00028-022-00859-7
apa: Dello Schiavo, L., & Wirth, M. (2023). Ergodic decompositions of Dirichlet
forms under order isomorphisms. Journal of Evolution Equations. Springer
Nature. https://doi.org/10.1007/s00028-022-00859-7
chicago: Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of
Dirichlet Forms under Order Isomorphisms.” Journal of Evolution Equations.
Springer Nature, 2023. https://doi.org/10.1007/s00028-022-00859-7.
ieee: L. Dello Schiavo and M. Wirth, “Ergodic decompositions of Dirichlet forms
under order isomorphisms,” Journal of Evolution Equations, 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.
mla: Dello Schiavo, Lorenzo, and Melchior Wirth. “Ergodic Decompositions of Dirichlet
Forms under Order Isomorphisms.” Journal of Evolution Equations, vol. 23,
no. 1, 9, Springer Nature, 2023, doi:10.1007/s00028-022-00859-7.
short: L. Dello Schiavo, M. Wirth, Journal of Evolution Equations 23 (2023).
date_created: 2023-01-08T23:00:53Z
date_published: 2023-01-01T00:00:00Z
date_updated: 2023-06-28T11:54:35Z
day: '01'
ddc:
- '510'
department:
- _id: JaMa
doi: 10.1007/s00028-022-00859-7
ec_funded: 1
external_id:
isi:
- '000906214600004'
file:
- access_level: open_access
checksum: 1f34f3e2cb521033de6154f274ea3a4e
content_type: application/pdf
creator: dernst
date_created: 2023-01-20T10:45:06Z
date_updated: 2023-01-20T10:45:06Z
file_id: '12325'
file_name: 2023_JourEvolutionEquations_DelloSchiavo.pdf
file_size: 422612
relation: main_file
success: 1
file_date_updated: 2023-01-20T10:45:06Z
has_accepted_license: '1'
intvolume: ' 23'
isi: 1
issue: '1'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
grant_number: E208
name: Configuration Spaces over Non-Smooth Spaces
- _id: 34c6ea2d-11ca-11ed-8bc3-c04f3c502833
grant_number: ESP156_N
name: Gradient flow techniques for quantum Markov semigroups
publication: Journal of Evolution Equations
publication_identifier:
eissn:
- 1424-3202
issn:
- 1424-3199
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Ergodic decompositions of Dirichlet forms under order isomorphisms
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 23
year: '2023'
...
---
_id: '11330'
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.
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)."
article_number: '19'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Wirth M. A dual formula for the noncommutative transport distance. Journal
of Statistical Physics. 2022;187(2). doi:10.1007/s10955-022-02911-9
apa: Wirth, M. (2022). A dual formula for the noncommutative transport distance.
Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02911-9
chicago: Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.”
Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02911-9.
ieee: M. Wirth, “A dual formula for the noncommutative transport distance,” Journal
of Statistical Physics, vol. 187, no. 2. Springer Nature, 2022.
ista: Wirth M. 2022. A dual formula for the noncommutative transport distance. Journal
of Statistical Physics. 187(2), 19.
mla: Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.”
Journal of Statistical Physics, vol. 187, no. 2, 19, Springer Nature, 2022,
doi:10.1007/s10955-022-02911-9.
short: M. Wirth, Journal of Statistical Physics 187 (2022).
date_created: 2022-04-24T22:01:43Z
date_published: 2022-04-08T00:00:00Z
date_updated: 2023-08-03T06:37:49Z
day: '08'
ddc:
- '510'
- '530'
department:
- _id: JaMa
doi: 10.1007/s10955-022-02911-9
ec_funded: 1
external_id:
isi:
- '000780305000001'
file:
- access_level: open_access
checksum: f3e0b00884b7dde31347a3756788b473
content_type: application/pdf
creator: dernst
date_created: 2022-04-29T11:24:23Z
date_updated: 2022-04-29T11:24:23Z
file_id: '11338'
file_name: 2022_JourStatisticalPhysics_Wirth.pdf
file_size: 362119
relation: main_file
success: 1
file_date_updated: 2022-04-29T11:24:23Z
has_accepted_license: '1'
intvolume: ' 187'
isi: 1
issue: '2'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 256E75B8-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '716117'
name: Optimal Transport and Stochastic Dynamics
publication: Journal of Statistical Physics
publication_identifier:
eissn:
- '15729613'
issn:
- '00224715'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: A dual formula for the noncommutative transport distance
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 187
year: '2022'
...
---
_id: '11916'
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.
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)."
article_number: '38'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Wirth M. Kac regularity and domination of quadratic forms. Advances in Operator
Theory. 2022;7(3). doi:10.1007/s43036-022-00199-w
apa: Wirth, M. (2022). Kac regularity and domination of quadratic forms. Advances
in Operator Theory. Springer Nature. https://doi.org/10.1007/s43036-022-00199-w
chicago: Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” Advances
in Operator Theory. Springer Nature, 2022. https://doi.org/10.1007/s43036-022-00199-w.
ieee: M. Wirth, “Kac regularity and domination of quadratic forms,” Advances
in Operator Theory, vol. 7, no. 3. Springer Nature, 2022.
ista: Wirth M. 2022. Kac regularity and domination of quadratic forms. Advances
in Operator Theory. 7(3), 38.
mla: Wirth, Melchior. “Kac Regularity and Domination of Quadratic Forms.” Advances
in Operator Theory, vol. 7, no. 3, 38, Springer Nature, 2022, doi:10.1007/s43036-022-00199-w.
short: M. Wirth, Advances in Operator Theory 7 (2022).
date_created: 2022-08-18T07:22:24Z
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publication_identifier:
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title: Kac regularity and domination of quadratic forms
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---
_id: '9627'
abstract:
- lang: eng
text: "We compute the deficiency spaces of operators of the form \U0001D43B\U0001D434⊗̂
\U0001D43C+\U0001D43C⊗̂ \U0001D43B\U0001D435, for symmetric \U0001D43B\U0001D434
and self-adjoint \U0001D43B\U0001D435. 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 \U0001D43B\U0001D435 having discrete,
non-degenerate spectrum."
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.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Daniel
full_name: Lenz, Daniel
last_name: Lenz
- first_name: Timon
full_name: Weinmann, Timon
last_name: Weinmann
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
citation:
ama: Lenz D, Weinmann T, Wirth M. Self-adjoint extensions of bipartite Hamiltonians.
Proceedings of the Edinburgh Mathematical Society. 2021;64(3):443-447.
doi:10.1017/S0013091521000080
apa: Lenz, D., Weinmann, T., & Wirth, M. (2021). Self-adjoint extensions of
bipartite Hamiltonians. Proceedings of the Edinburgh Mathematical Society.
Cambridge University Press. https://doi.org/10.1017/S0013091521000080
chicago: Lenz, Daniel, Timon Weinmann, and Melchior Wirth. “Self-Adjoint Extensions
of Bipartite Hamiltonians.” Proceedings of the Edinburgh Mathematical Society.
Cambridge University Press, 2021. https://doi.org/10.1017/S0013091521000080.
ieee: D. Lenz, T. Weinmann, and M. Wirth, “Self-adjoint extensions of bipartite
Hamiltonians,” Proceedings of the Edinburgh Mathematical Society, vol.
64, no. 3. Cambridge University Press, pp. 443–447, 2021.
ista: Lenz D, Weinmann T, Wirth M. 2021. Self-adjoint extensions of bipartite Hamiltonians.
Proceedings of the Edinburgh Mathematical Society. 64(3), 443–447.
mla: Lenz, Daniel, et al. “Self-Adjoint Extensions of Bipartite Hamiltonians.” Proceedings
of the Edinburgh Mathematical Society, vol. 64, no. 3, Cambridge University
Press, 2021, pp. 443–47, doi:10.1017/S0013091521000080.
short: D. Lenz, T. Weinmann, M. Wirth, Proceedings of the Edinburgh Mathematical
Society 64 (2021) 443–447.
date_created: 2021-07-04T22:01:24Z
date_published: 2021-08-01T00:00:00Z
date_updated: 2023-08-17T07:12:05Z
day: '01'
department:
- _id: JaMa
doi: 10.1017/S0013091521000080
external_id:
arxiv:
- '1912.03670'
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- '000721363700003'
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- iso: eng
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month: '08'
oa: 1
oa_version: Published Version
page: 443-447
publication: Proceedings of the Edinburgh Mathematical Society
publication_identifier:
eissn:
- 1464-3839
issn:
- 0013-0915
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Self-adjoint extensions of bipartite Hamiltonians
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 64
year: '2021'
...
---
_id: '9973'
abstract:
- lang: eng
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.
acknowledgement: Both authors would like to thank Jan Maas for fruitful discussions
and helpful comments.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
- first_name: Haonan
full_name: Zhang, Haonan
id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
last_name: Zhang
citation:
ama: Wirth M, Zhang H. Complete gradient estimates of quantum Markov semigroups.
Communications in Mathematical Physics. 2021;387:761–791. doi:10.1007/s00220-021-04199-4
apa: Wirth, M., & Zhang, H. (2021). Complete gradient estimates of quantum Markov
semigroups. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-021-04199-4
chicago: Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum
Markov Semigroups.” Communications in Mathematical Physics. Springer Nature,
2021. https://doi.org/10.1007/s00220-021-04199-4.
ieee: M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,”
Communications in Mathematical Physics, vol. 387. Springer Nature, pp.
761–791, 2021.
ista: Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups.
Communications in Mathematical Physics. 387, 761–791.
mla: Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum
Markov Semigroups.” Communications in Mathematical Physics, vol. 387, Springer
Nature, 2021, pp. 761–791, doi:10.1007/s00220-021-04199-4.
short: M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791.
date_created: 2021-08-30T10:07:44Z
date_published: 2021-08-30T00:00:00Z
date_updated: 2023-08-11T11:09:07Z
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department:
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doi: 10.1007/s00220-021-04199-4
ec_funded: 1
external_id:
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- '000691214200001'
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keyword:
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name: IST Austria Open Access Fund
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title: Complete gradient estimates of quantum Markov semigroups
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