# A. Jeribi

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Articles: 2

### Essential approximate point and essential defect spectrum of a sequence of linear operators in Banach spaces

MFAT 25 (2019), no. 4, 373-380

373-380

This paper is devoted to an investigation of the relationship between the essential approximate point spectrum (respectively, the essential defect spectrum) of a sequ\-ence of closed linear operators $(T_n)_{n\in\mathbb{N}}$ on a Banach space $X$, and the essential approximate point spectrum (respectively, the essential defect spectrum) of a linear operator $T$ on $X$, where $(T_n)_{n\in\mathbb{N}}$ converges to $T$, in the case of convergence in generalized sense as well as in the case of the convergence compactly

### Measure of noncompactness, essential approximation and defect pseudospectrum

MFAT 25 (2019), no. 1, 1-11

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.