An Aglertype model theorem for C_{0}semigroups of Hilbert space contractions
(2016) In Journal of the London Mathematical Society 93(2). p.420438 Abstract
 We investigate suitable conditions for a C0semigroup (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 γhypercontractive 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 γhypercontractive. 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 C0semigroup (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 γhypercontractive 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 γhypercontractive. 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:
http://lup.lub.lu.se/record/7a47158876dd465280e6e465ac0ff15f
 author
 Rydhe, Eskil ^{LU}
 organization
 publishing date
 201604
 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
 00246107
 DOI
 10.1112/jlms/jdv067
 language
 English
 LU publication?
 yes
 id
 7a47158876dd465280e6e465ac0ff15f
 alternative location
 http://jlms.oxfordjournals.org/cgi/content/full/jdv067? ijkey=NWdeYquUguXQG50&keytype=ref
 date added to LUP
 20160419 09:32:39
 date last changed
 20180107 11:10:23
@article{7a47158876dd465280e6e465ac0ff15f, abstract = {We investigate suitable conditions for a C0semigroup (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 γhypercontractive 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 γhypercontractive. 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 = {00246107}, language = {eng}, number = {2}, pages = {420438}, publisher = {Oxford University Press}, series = {Journal of the London Mathematical Society}, title = {An Aglertype model theorem for <em style="margin: 0px; padding: 0px; border: 0px; outlinestyle: none; fontsize: inherit; fontfamily: inherit; lineheight: inherit; textalign: inherit; verticalalign: baseline;">C</em><sub style="margin: 0px; padding: 0px; border: 0px; outlinestyle: none; fontstyle: inherit; fontsize: 0.85em; fontfamily: inherit; lineheight: 0; textalign: inherit;">0</sub>semigroups of Hilbert space contractions}, url = {http://dx.doi.org/10.1112/jlms/jdv067}, volume = {93}, year = {2016}, }