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A characterization of the essential approximation pseudospectrum on a Banach space

Ammar Aymen (University of Sfax, Faculty of Sciences of Sfax, Department of Mathematics, Sfax, Tunisia)
Jeribi Aref (University of Sfax, Faculty of Sciences of Sfax, Department of Mathematics, Sfax, Tunisia)
Mahfoudhi Kamel (University of Sfax, Faculty of Sciences of Sfax, Department of Mathematics, Sfax, Tunisia)

One impetus for writing this paper is the issue of approximation pseudospectrum introduced by M. P. H.Wolff in the journal of approximation theory (2001). The latter study motivates us to investigate the essential approximation pseudospectrum of closed, densely defined linear operators on a Banach space. We begin by defining it and then we focus on the characterization, the stability and some properties of these pseudospectra.

Keywords: Approximation pseudospectrum, essential approximation pseudospectrum