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

Abstract

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.

Key words: Pseudo spectrum, Essential pseudospectra, strict singular operators, polynomially non-strict singular operators.

Full Text

Article Information

Title	Spectral Properties of Essential Pseudospectra under Polynomially Non-Strict Singular Perturbations
Source	Methods Funct. Anal. Topology, Vol. 31 (2025), no. 3, 204-221
DOI	10.31392/MFAT-npu26_3.2025.05
Milestones	Received 16/04/2024; Revised 01/10/2025
Copyright	The Author(s) 2025 (CC BY-SA)

Authors Information

Bilel Elgabeur
University of Aix-Marseille, France

Citation Example

Bilel Elgabeur, Spectral Properties of Essential Pseudospectra under Polynomially Non-Strict Singular Perturbations, Methods Funct. Anal. Topology 31 (2025), no. 3, 204-221.

BibTex

@article {MFAT2125,
    AUTHOR = {Bilel Elgabeur},
     TITLE = {Spectral Properties of Essential Pseudospectra under Polynomially Non-Strict Singular Perturbations},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {31},
      YEAR = {2025},
    NUMBER = {3},
     PAGES = {204-221},
      ISSN = {1029-3531},
       DOI = {10.31392/MFAT-npu26_3.2025.05},
       URL = {https://mfat.imath.kiev.ua/article/?id=2125},
}

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