Generalized Drazin-meromorphic pseudospectrum for multivalued linear relation

Abstract

In this paper, we shall investigate such kinds of operators and corresponding
spectra, the generalized Drazin-meromorphic pseudospectrum. More specifically,
the generalized Drazin-meromorphic pseudospectrum for a linear relation on
a Banach space is studied. We also make several observations about the level
set of the generalized Drazin-meromorphic pseudospectrum of linear relations.
Furthermore, it is shown that pseudospectrum has no isolated points, has a finite
number of connected components and each component contains an element from
the generalized Drazin-meromorphic spectrum.