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

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 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 L 0 .The results are formulated in terms of some denseness conditions on the topological dual space.