Weak demicompactness involving measures of weak noncompactness and invariance of the essential spectrum

Abstract

In this paper, we show that an unbounded weakly S0-demicompact
linear operator T, introduced in [16], acting on a Banach space, can be character-
ized by some measures of weak noncompactness. Moreover, some other quantities
related to these measures provide sucient conditions to the operator T to be S0-
demicompact. Our results are illustrated to discuss the relationship with Fredholm
and upper semi-Fredholm operators as well as the stability of the essential spectrum
of T.