An Agler-type model theorem for C0-semigroups of Hilbert space contractions

Research output: Contribution to journalArticlepeer-review

4 Citations (SciVal)

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.
Original languageEnglish
Pages (from-to)420-438
Number of pages19
JournalJournal of the London Mathematical Society
Volume93
Issue number2
DOIs
Publication statusPublished - 2016 Apr

Subject classification (UKÄ)

  • Mathematical Analysis

Fingerprint

Dive into the research topics of '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'. Together they form a unique fingerprint.

Cite this