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Mediterranean Journal of Mathematics

, Volume 10, Issue 3, pp 1487–1496 | Cite as

On the B-Fredholm Alternative

  • Mohammed Berkani
Article

Abstract

The aim of this paper is to give an extended version of the Fredholm alternative, by including the B-Fredholm case. Thus if T a B-Fredholm operator acting on a Banach space, we study equations of the type T(x) =  y, for x, y elements of the range R(T n ) of T for \({n \in \mathbb{N}}\). In this study we include the case when 0 is a pole of infinite rank of the resolvent of T. Preliminarily, we define unbounded closed B-Fredholm operators on Banach spaces.

Mathematics Subject Classification (2010)

47A53 47A55 

Keywords

Unbounded B-Fredholm operators index Drazin inverse Fredholm alternative 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of mathematics, Science facultyUniversity Mohammed IOujdaMorocco

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