B. Elgabeur

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Articles: 1

Spectral Properties of Essential Pseudospectra under Polynomially Non-Strict Singular Perturbations

MFAT 31 (2025), no. 3, 204-221

204-221

This paper investigates the essential pseudospectra of closed linear operators in Banach spaces, focusing on perturbations induced by polynomially non-strictly singular operators, a class that extends the concept of polynomially strictly singular operators. New results are presented regarding the behavior of the essential pseudospectra under these perturbations. In particular, we explore the impact on the left (resp. right) Weyl and Fredholm essential pseudospectra. Additionally, we examine the essential pseudospectra of the sum of two bounded linear operators and apply the results to characterize the pseudo-Fredholm spectra of \( 2 \times 2 \) block operator matrices.

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