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