In this paper, we introduce and study the essential pseudospectra of closed, densely defined linear operators in the Banach space. We start by giving the definition and we investigate the characterization, the stability and some properties of these essential pseudospectra. Mathematics Subject Classification 47A53 • 47A55 • 54B35 • 47A13 1 Introduction Let X and Y be two Banach spaces. We denote by L(X, Y) resp., C(X, Y) the set of all bounded (resp., closed, densely defined) linear operators from X into Y and we denote by K(X, Y
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.
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