Demicompactness Results for Strongly Continuous Semigroups, Generators and Resolvents

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Abstract

Let \((U(t))_ {t\ge 0}\) be a strongly continuous semigroup of bounded linear operators on a Banach space X and B be a bounded operator on X. In this paper, we develop some aspects of the theory of semigroup for which U(t)B (respectively, BU(t), BU(t)B) is demicompact for some (respectively, every) \(t>0\). In addition, we study the demicompactness of similar, subspace and product semigroups. We also investigate the demicompactness of the resolvent. We close this paper by giving some conditions guaranteeing the demicompactness of a generator of a strongly continuous semigroup in a Hilbert space.

Keywords

Strongly continuous semigroup Demicompact linear operator Fredholm operator Hilbert space 

Mathematics Subject Classification

47D06 47A13 

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Sciences of SfaxUniversity of SfaxSfaxTunisia

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