Open Access

# Measure of noncompactness, essential approximation and 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.

Key words: Measures of noncompactness, essential approximation pseudospectrum, essential defect pseudospectrum.

### Article Information

 Title Measure of noncompactness, essential approximation and defect pseudospectrum Source Methods Funct. Anal. Topology, Vol. 25 (2019), no. 1, 1-11 Milestones Received 11/01/2018; Revised 10/04/2018 Copyright The Author(s) 2019 (CC BY-SA)

### Authors Information

Aymen Ammar
Department of Mathematics, University of Sfax, Faculty of Sciences of Sfax, Route de soukra Km 3.5, B.P. 1171, 3000, Sfax, Tunisia

Aref Jeribi
Department of Mathematics, University of Sfax, Faculty of Sciences of Sfax, Route de soukra Km 3.5, B.P. 1171, 3000, Sfax, Tunisia

Kamel Mahfoudhi
Department of Mathematics, University of Sfax, Faculty of Sciences of Sfax, Route de soukra Km 3.5, B.P. 1171, 3000, Sfax, Tunisia

### Citation Example

Aymen Ammar, Aref Jeribi, and Kamel Mahfoudhi, Measure of noncompactness, essential approximation and defect pseudospectrum, Methods Funct. Anal. Topology 25 (2019), no. 1, 1-11.

### BibTex

@article {MFAT1139,
AUTHOR = {Aymen Ammar and Aref Jeribi and Kamel Mahfoudhi},
TITLE = {Measure of noncompactness, essential approximation and defect pseudospectrum},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {25},
YEAR = {2019},
NUMBER = {1},
PAGES = {1-11},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=1139},
}

Coming Soon.