Essential pseudospectra involving demicompact and pseudodemicompact operators and some perturbation results

Fatma Brahim, Aref Jeribi, Bilel Krichen
2019 Filomat  
In this paper, we study the essential and the structured essential pseudospectra of closed densely defined linear operators acting on a Banach space X. We start by giving a refinement and investigating the stability of these essential pseudospectra by means of the class of demicompact linear operators. Moreover, we introduce the notion of pseudo demicompactness and we study its relationship with pseudo upper semi-Fredholm operators. Some stability results for the Gustafson essential
more » ... sential pseudospectrum involving pseudo demicompact operators is given.
doi:10.2298/fil1908519b fatcat:4j4imi4hirajla26puzppwzq2a