An Agler-type model theorem for C0-semigroups of Hilbert space contractions
Författare
Summary, in English
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.
Avdelning/ar
- Matematik (naturvetenskapliga fakulteten)
- Harmonic Analysis and Applications
Publiceringsår
2016-04
Språk
Engelska
Sidor
420-438
Publikation/Tidskrift/Serie
Journal of the London Mathematical Society
Volym
93
Issue
2
Länkar
Dokumenttyp
Artikel i tidskrift
Förlag
Oxford University Press
Ämne
- Mathematical Analysis
Status
Published
Forskningsgrupp
- Harmonic Analysis and Applications
ISBN/ISSN/Övrigt
- ISSN: 0024-6107