RELATIVE ESSENTIAL SPECTRA INVOLVING RELATIVE DEMICOMPACT UNBOUNDED LINEAR OPERATORS

doi:10.1016/S0252-9602(14)60027-8

Abstract

Abstract:

In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation
results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter´s and approximate essential spectrum.

Key words: Demicompact linear operator, relative essential spectrum, Fredholm and semi-Fredholm operators, measure of noncompactness

CLC Number:

47A10

Bilel KRICHEN. RELATIVE ESSENTIAL SPECTRA INVOLVING RELATIVE DEMICOMPACT UNBOUNDED LINEAR OPERATORS[J].Acta mathematica scientia,Series B, 2014, 34(2): 546-556.

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