---
_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.
    <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>
  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>
  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>.
  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.
  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.” <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>.
  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'
  isi:
  - '000721363700003'
intvolume: '        64'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1017/S0013091521000080
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'
...