Spectral Characteristics of A-right Generalized Weakly Demicompact Operators

Abstract

In this research work, the central focus is upon elaborating certain results in Banach spaces for a new notion called A-right ascent of linear operators (where A is a given operator) which generalize an important notion in operator theory: ascent. Furthermore, if A is a bounded linear operator, we investigate the concept of A-right generalized weakly demicompact operators which in turn generalize the concept of generalized weakly demicompact operators introduced in [8]. In particular, a characterization using upper semi-Browder spectrum is set forward. Additionally, we identify some sufficient conditions on the inputs of a closable block operator matrix to ensure the generalized weak demicompactness of its closure. Moreover, some theorems in this paper generalize multiple known ones in the literature in particular [8].