Remarks on embeddable semigroups in groups and a generalization of some Cuthbert's results

Khalid Latrach and Abdelkader Dehici

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-11

Abstract:

Let ( U ( t ) ) t ≥ 0 be a C 0 -semigroup of bounded linear operators on a Banach space X . In this paper, we establish that if, for some t 0 > 0 , U ( t 0 ) is a Fredholm (resp., semi-Fredholm) operator, then ( U ( t ) ) t ≥ 0 is a Fredholm (resp., semi-Fredholm) semigroup. Moreover, we give a necessary and sufficient condition guaranteeing that ( U ( t ) ) t ≥ 0 can be imbedded in a C 0 -group on X . Also we study semigroups which are near the identity in the sense that there exists t 0 > 0 such that U ( t 0 ) − I ∈ 𝒥 ( X ) , where 𝒥 ( X ) is an arbitrary closed two-sided ideal contained in the set of Fredholm perturbations. We close this paper by discussing the case where 𝒥 ( X ) is replaced by some subsets of the set of polynomially compact perturbations.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:580140

DOI: 10.1155/S0161171203011839

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