Operator theoretic properties of semigroups in terms of their generators

• Autorzy: S. Blunck , L. Weis
• Języki publikacji: EN

Abstrakty

EN

Let $(T_{t})$ be a C₀ semigroup with generator A on a Banach space X and let 𝓐 be an operator ideal, e.g. the class of compact, Hilbert-Schmidt or trace class operators. We show that the resolvent R(λ,A) of A belongs to 𝓐 if and only if the integrated semigroup $S_{t}: = ∫_{0}^{t} T_{s}ds$ belongs to 𝓐. For analytic semigroups, $S_{t} ∈ 𝓐$ implies $T_{t} ∈ 𝓐$, and in this case we give precise estimates for the growth of the 𝓐-norm of $T_{t}$ (e.g. the trace of $T_{t}$) in terms of the resolvent growth and the imbedding D(A) ↪ X.

Kategorie tematyczne

• 47D06: One-parameter semigroups and linear evolution equations
• 47A60: Functional calculus
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 146
• Numer: 1
• Strony: 35-54

Daty

wydano

2001

Twórcy

autor

S. Blunck

• Mathematisches Institut I, Universität Karlsruhe, Englerstr. 2, D-76128 Karlsruhe, Germany

autor

L. Weis

• Mathematisches Institut I, Universität Karlsruhe, Englerstr. 2, D-76128 Karlsruhe, Germany

Identyfikatory

DOI

10.4064/sm146-1-3