Measure of noncompactness, essential approximation and defect pseudospectrum

Authors

  • A. Ammar Department of Mathematics, University of Sfax, Faculty of Sciences of Sfax, Route de soukra Km 3.5, B.P. 1171, 3000, Sfax, Tunisia
  • A. Jeribi Department of Mathematics, University of Sfax, Faculty of Sciences of Sfax, Route de soukra Km 3.5, B.P. 1171, 3000, Sfax, Tunisia
  • K. Mahfoudhi Department of Mathematics, University of Sfax, Faculty of Sciences of Sfax, Route de soukra Km 3.5, B.P. 1171, 3000, Sfax, Tunisia

DOI:

Keywords:

Measures of noncompactness, essential approximation pseudospectrum, essential defect pseudospectrum

Abstract

The scope of the present research is to establish some findings concerning the essential approximation pseudospectra and the essential defect pseudospectra of closed, densely defined linear operators in a Banach space, building upon the notion of the measure of noncompactness. We start by giving a refinement of the definition of the essential approximation pseudospectra and that of the essential defect pseudospectra by means of the measure of noncompactness. From these characterizations we shall deduce several results and we shall give sufficient conditions on the perturbed operator to have its invariance.

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Published

2019-03-25

Issue

Vol. 25 No. 1 (2019)

Section

Articles

How to Cite

Ammar, A., et al. “Measure of Noncompactness, Essential Approximation and Defect Pseudospectrum”. Methods of Functional Analysis and Topology, vol. 25, no. 1, Mar. 2019, pp. 1-11, https://zen.imath.kiev.ua/index.php/mfat/article/view/708.