An Agler-type model theorem for C0-semigroups of Hilbert space contractions
(2016) In Journal of the London Mathematical Society 93(2). p.420-438- Abstract
- We investigate suitable conditions for a C0-semigroup (T(t))t≥0 of Hilbert space contractions to be unitarily equivalent to the restriction of the adjoint shift semigroup (S∗γ(t))t≥0 to an invariant subspace of the standard weighted Bergman space Aγ−2(C+,K). It turns out that (T(t))t≥0 admits a model by (S∗γ(t))t≥0 if and only if its cogenerator is γ-hypercontractive and limt→0T(t)=0 in strong operator topology. We then discuss how such semigroups can be characterized without involving the cogenerator. A sufficient condition is that, for each t>0, the operator T(t) is γ-hypercontractive. Surprisingly, this condition is necessary if and only if γ is integer. The paper is concluded with a conjecture that would imply a more symmetric... (More)
- We investigate suitable conditions for a C0-semigroup (T(t))t≥0 of Hilbert space contractions to be unitarily equivalent to the restriction of the adjoint shift semigroup (S∗γ(t))t≥0 to an invariant subspace of the standard weighted Bergman space Aγ−2(C+,K). It turns out that (T(t))t≥0 admits a model by (S∗γ(t))t≥0 if and only if its cogenerator is γ-hypercontractive and limt→0T(t)=0 in strong operator topology. We then discuss how such semigroups can be characterized without involving the cogenerator. A sufficient condition is that, for each t>0, the operator T(t) is γ-hypercontractive. Surprisingly, this condition is necessary if and only if γ is integer. The paper is concluded with a conjecture that would imply a more symmetric characterization. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/7a471588-76dd-4652-80e6-e465ac0ff15f
- author
- Rydhe, Eskil LU
- organization
- publishing date
- 2016-04
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of the London Mathematical Society
- volume
- 93
- issue
- 2
- pages
- 19 pages
- publisher
- Oxford University Press
- external identifiers
-
- wos:000374188000008
- scopus:84971602173
- ISSN
- 0024-6107
- DOI
- 10.1112/jlms/jdv067
- language
- English
- LU publication?
- yes
- id
- 7a471588-76dd-4652-80e6-e465ac0ff15f
- alternative location
- http://jlms.oxfordjournals.org/cgi/content/full/jdv067? ijkey=NWdeYquUguXQG50&keytype=ref
- date added to LUP
- 2016-04-19 09:32:39
- date last changed
- 2022-01-30 02:44:25
@article{7a471588-76dd-4652-80e6-e465ac0ff15f,
abstract = {{We investigate suitable conditions for a C0-semigroup (T(t))t≥0 of Hilbert space contractions to be unitarily equivalent to the restriction of the adjoint shift semigroup (S∗γ(t))t≥0 to an invariant subspace of the standard weighted Bergman space Aγ−2(C+,K). It turns out that (T(t))t≥0 admits a model by (S∗γ(t))t≥0 if and only if its cogenerator is γ-hypercontractive and limt→0T(t)=0 in strong operator topology. We then discuss how such semigroups can be characterized without involving the cogenerator. A sufficient condition is that, for each t>0, the operator T(t) is γ-hypercontractive. Surprisingly, this condition is necessary if and only if γ is integer. The paper is concluded with a conjecture that would imply a more symmetric characterization.}},
author = {{Rydhe, Eskil}},
issn = {{0024-6107}},
language = {{eng}},
number = {{2}},
pages = {{420--438}},
publisher = {{Oxford University Press}},
series = {{Journal of the London Mathematical Society}},
title = {{An Agler-type model theorem for <em style="margin: 0px; padding: 0px; border: 0px; outline-style: none; font-size: inherit; font-family: inherit; line-height: inherit; text-align: inherit; vertical-align: baseline;">C</em><sub style="margin: 0px; padding: 0px; border: 0px; outline-style: none; font-style: inherit; font-size: 0.85em; font-family: inherit; line-height: 0; text-align: inherit;">0</sub>-semigroups of Hilbert space contractions}},
url = {{http://dx.doi.org/10.1112/jlms/jdv067}},
doi = {{10.1112/jlms/jdv067}},
volume = {{93}},
year = {{2016}},
}