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Some Conditions for a C0-Semigroup to Be Asymptotically Finite-Dimensional

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Abstract

We study the class of bounded C 0-semigroups T=(T t ) t≥0 on a Banach space X satisfying the asymptotic finite dimensionality condition: codim X 0(T)<∞, where X 0(T):={x∈ X:limt→∞ ❘T t x❘=0}. We prove a theorem which provides some necessary and sufficient conditions for asymptotic finite dimensionality.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk

    E. Yu. Emel'yanov

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  1. E. Yu. Emel'yanov
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Emel'yanov, E.Y. Some Conditions for a C0-Semigroup to Be Asymptotically Finite-Dimensional. Siberian Mathematical Journal 44, 793–796 (2003). https://doi.org/10.1023/A:1025976401206

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