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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Issue 2 (Special CSMT 2023)   > Article

ε-Pseudo Weak-Demicompactness for 2 × 2 Block Operator Matrices

ε-Pseudo faible-demi-compacité pour les opérateurs matriciels 2 × 2 en block


Ines Chtourou
University of Sfax
Tunisia

Bilel Krichen
University of Sfax
Tunisia



Published on 7 March 2024   DOI : 10.21494/ISTE.OP.2024.1098

Abstract

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The purpose of this paper is to give some properties for the so-called ε-pseudo weakly demicompact linear operators acting on Banach spaces. Some sufficient conditions on the entries of an unbounded 2 × 2 block operator matrix L0 ensuring its ε-pseudo weak demicompactness are provided. In addition, we develop, in the bounded case, the class of ε-pseudo Fredholm perturbation to investigate the essential pseudo-spectra of L0. The results are formulated in terms of some denseness conditions on the topological dual space.

The purpose of this paper is to give some properties for the so-called ε-pseudo weakly demicompact linear operators acting on Banach spaces. Some sufficient conditions on the entries of an unbounded 2 × 2 block operator matrix L0 ensuring its ε-pseudo weak demicompactness are provided. In addition, we develop, in the bounded case, the class of ε-pseudo Fredholm perturbation to investigate the essential pseudo-spectra of L0. The results are formulated in terms of some denseness conditions on the topological dual space.

Demicompact linear operator Pseudo-Fredholm Perturbation theory Essential pseudo-spectra

Demicompact linear operator Pseudo-Fredholm Perturbation theory Essential pseudo-spectra

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