On the criteria of a measure of non-strict cosingularity in the description of spectral properties of operator matrix-Reference-Cited by-同舟云学术

On the criteria of a measure of non-strict cosingularity in the description of spectral properties of operator matrix

Published:2024-06-11 Issue: Volume: Page:
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Bouzidi Sana¹,Walha Ines¹

Affiliation:

1. Department of Mathematics , Faculty of Sciences of Sfax , University of Sfax , BP 1171 , Sfax 3000 , Tunisia

Abstract

Abstract In this paper, we are interested to formulate new assumptions on the entries of an unbounded 3 × 3

3\times 3

block operator matrix defined with a maximal domain on the product of Banach spaces guaranteeing its corresponding Frobenius–Schur formula. Our approach allows us to derive some original stability results intervening in the theory of perturbed lower semi-Fredholm operators involving the concept of a measure of non-strict cosingularity perturbation. A new technique is presented to investigate the Weidmann and defect essential spectra of the closure of such model of operator matrix via new criterion of perturbation.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2024-2029/pdf

Reference27 articles.

1. F. V. Atkinson, H. Langer, R. Mennicken and A. A. Shkalikov, The essential spectrum of some matrix operators, Math. Nachr. 167 (1994), 5–20.

2. A. Bahloul and I. Walha, Generalized Drazin invertibility of operator matrices, Numer. Funct. Anal. Optim. 43 (2022), no. 16, 1836–1847.

3. J. A. Burns and R. H. Fabiano, Feedback control of a hyperbolic partial-differential equation with viscoelastic damping, Control Theory Adv. Tech. 5 (1989), no. 2, 157–188.

4. S. Charfi, A. Elleuch and I. Walha, Spectral theory involving the concept of quasi-compact perturbations, Mediterr. J. Math. 17 (2020), no. 1, Paper No. 32.

5. S. Charfi and I. Walha, On relative essential spectra of block operator matrices and application, Bull. Korean Math. Soc. 53 (2016), no. 3, 681–698.