Operator theoretic properties of semigroups in terms of their generators

S. Blunck; L. Weis

S. Blunck ; L. Weis

Studia Mathematica, Tome 147 (2001), p. 35-54 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $(T_{t})$ be a C₀ semigroup with generator A on a Banach space X and let 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 if and only if the integrated semigroup $S_{t} : = \int_{0}^{t} T_{s} d s$ belongs to . For analytic semigroups, $S_{t} \in$ implies $T_{t} \in$ , and in this case we give precise estimates for the growth of the -norm of $T_{t}$ (e.g. the trace of $T_{t}$ ) in terms of the resolvent growth and the imbedding D(A) ↪ X.

Publié le : 2001-01-01

Zbl 1011.47030

EUDML-ID : urn:eudml:doc:284933

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     year = {2001},
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S. Blunck; L. Weis. Operator theoretic properties of semigroups in terms of their generators. Studia Mathematica, Tome 147 (2001) pp. 35-54. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-1-3/