Measures of noncompactness and essential pseudospectra on Banach space

Abstract

In this research article, we work with the notion of the measures of noncompactness in order to establish some results concerning the essential pseudospectra of closed, densely defined linear operators in the Banach space. We start by giving a refinement of the definition of the essential pseudospectra by means of the measure of noncompactness, and we give sufficient conditions on the perturbed operator to have its invariance. Copyright © 2013 John Wiley & Sons, Ltd.