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Index for generalized Fredholm operators and generalized perturbation theory

  • Rabeb Aydi , Imen Ferjani and Bilel Krichen EMAIL logo
Published/Copyright: May 3, 2023
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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.

MSC 2020: 47A53; 47A10; 47A55

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Received: 2022-09-27
Revised: 2022-12-06
Accepted: 2022-12-12
Published Online: 2023-05-03
Published in Print: 2023-08-01

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