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

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