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

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Sammanfattning

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.
Originalspråkengelska
Sidor (från-till)420-438
Antal sidor19
TidskriftJournal of the London Mathematical Society
Volym93
Utgåva2
DOI
StatusPublished - 2016 apr

Ämnesklassifikation (UKÄ)

  • Matematisk analys

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