Index for generalized Fredholm operators and generalized perturbation theory

Author:

Aydi Rabeb1,Ferjani Imen1,Krichen Bilel1

Affiliation:

1. Department of Mathematics , Faculty of Sciences of Sfax , University of Sfax , Road Soukra Km 3.5, B.P. 1171, 3000 , Sfax , Tunisia

Abstract

Abstract In this paper, we develop some generalized Fredholm perturbation results for bounded linear operators acting on non-reflexive Banach spaces satisfying certain conditions. Furthermore, we investigate the stability of the generalized Schechter S-essential spectrum by means of the so-called generalized Fredholm index. This concept is introduced as a semigroup homomorphism satisfying certain properties. Some generalized Fredholm results for block operator matrices acting on a non-reflexive product of two Banach spaces are also developed.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference24 articles.

1. P. Aiena, Fredholm and Local Spectral Theory, with Applications to Multipliers, Kluwer Academic, Dordrecht, 2004.

2. F. Albiac and N. J. Kalton, Topics in Banach Space Theory, Grad. Texts in Math. 233, Springer, New York, 2006.

3. K. Astala, On measures of noncompactness and ideal variations in Banach spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. Diss. 29 (1980), 1–42.

4. A. Azzouz, M. Beghdadi and B. Krichen, g-Riesz operators and their spectral properties, Adv. Oper. Theory 7 (2022), no. 2, Paper No. 18.

5. A. Azzouz, M. Beghdadi and B. Krichen, Generalized relative essential spectra, Filomat 36 (2022), no. 8, 2657–2673.

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