Spectral Properties Involving Generalized Weakly Demicompact Operators

Abstract

In this paper, we investigate the concept of generalized weakly demicompact operators with respect to weakly closed densely defined linear operators. We give their relationship with Fredholm and upper semi-Fredholm operators. In particular a characterization by means of upper semi-Browder spectrum is given. Moreover, we provide some sufficient conditions on the inputs of a closable block operator matrix to ensure the generalized weak demicompactness of its closure. Our results generalize many known ones in the literature.