Recurrent strongly continuous operator families on Banach space

Abstract

In this paper, we analyze recurrent $C_0$-semigroups of bounded operators on Banach spaces. We also introduce the notion of a (uniformly) $C_0$-rigid semigroups of bounded operators and give a structural characterization of them. A characterization of a Li-Yorke chaoticity of the translation semigroup $(T(t){)}_{t\ge 0}$ on weighted spaces of integrable functions and continuous functions in terms of admissible weight function is given. The recurrent $C_0$-semigroups induced by semiflows are characterized on the spaces of integrable functions and of spaces of continuous functions.

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