Convergence of operators with deficiency indices (k, k) and of their self-adjoint extensions

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Standard

Convergence of operators with deficiency indices (k, k) and of their self-adjoint extensions. / Bjerg, August.

I: Annales Henri Poincare, 2024.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Bjerg, A 2024, 'Convergence of operators with deficiency indices (k, k) and of their self-adjoint extensions', Annales Henri Poincare. https://doi.org/10.1007/s00023-023-01397-9

APA

Bjerg, A. (2024). Convergence of operators with deficiency indices (k, k) and of their self-adjoint extensions. Annales Henri Poincare. https://doi.org/10.1007/s00023-023-01397-9

Vancouver

Bjerg A. Convergence of operators with deficiency indices (k, k) and of their self-adjoint extensions. Annales Henri Poincare. 2024. https://doi.org/10.1007/s00023-023-01397-9

Author

Bjerg, August. / Convergence of operators with deficiency indices (k, k) and of their self-adjoint extensions. I: Annales Henri Poincare. 2024.

Bibtex

@article{c45bdc8f40c94937ae99ea959e69c57f,
title = "Convergence of operators with deficiency indices (k, k) and of their self-adjoint extensions",
abstract = "We consider an abstract sequence {An}n=1∞ of closed symmetric operators on a separable Hilbert space H . It is assumed that all An {\textquoteright}s have equal deficiency indices (k, k) and thus self-adjoint extensions {Bn}n=1∞ exist and are parametrized by partial isometries {Un}n=1∞ on H according to von Neumann{\textquoteright}s extension theory. Under two different convergence assumptions on the An {\textquoteright}s we give the precise connection between strong resolvent convergence of the Bn {\textquoteright}s and strong convergence of the Un {\textquoteright}s. {\textcopyright} 2023, The Author(s).",
author = "August Bjerg",
year = "2024",
doi = "10.1007/s00023-023-01397-9",
language = "English",
journal = "Annales Henri Poincare",
issn = "1424-0637",
publisher = "Springer Basel AG",

}

RIS

TY - JOUR

T1 - Convergence of operators with deficiency indices (k, k) and of their self-adjoint extensions

AU - Bjerg, August

PY - 2024

Y1 - 2024

N2 - We consider an abstract sequence {An}n=1∞ of closed symmetric operators on a separable Hilbert space H . It is assumed that all An ’s have equal deficiency indices (k, k) and thus self-adjoint extensions {Bn}n=1∞ exist and are parametrized by partial isometries {Un}n=1∞ on H according to von Neumann’s extension theory. Under two different convergence assumptions on the An ’s we give the precise connection between strong resolvent convergence of the Bn ’s and strong convergence of the Un ’s. © 2023, The Author(s).

AB - We consider an abstract sequence {An}n=1∞ of closed symmetric operators on a separable Hilbert space H . It is assumed that all An ’s have equal deficiency indices (k, k) and thus self-adjoint extensions {Bn}n=1∞ exist and are parametrized by partial isometries {Un}n=1∞ on H according to von Neumann’s extension theory. Under two different convergence assumptions on the An ’s we give the precise connection between strong resolvent convergence of the Bn ’s and strong convergence of the Un ’s. © 2023, The Author(s).

U2 - 10.1007/s00023-023-01397-9

DO - 10.1007/s00023-023-01397-9

M3 - Journal article

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

ER -

ID: 380360053