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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 $$$\mathcal{L}_{0}$$$ 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 $$$\mathcal{L}_{0}$$$. 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 $$$\mathcal{L}_{0}$$$ 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 $$$\mathcal{L}_{0}$$$. 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