Mohammed Berkani

University Mohammed I

Title: B-Fredholm theory and Drazin invertibility 

Abstract: In this talk we will introduce the class of B-Fredholm operators, as a natural generalization of Fredholm operators.  While the invertibility in the Calkin algebra characterizes Fredholm operators, we show that Drazin invertibility in the algebra L(X)/ F_0(X), F_0(X) being the ideal of finite rank  operators, characterizes B-Fredholm operators.  Then we will answer a natural arising question: What are the properties of those operators whose image under the canonical homomorphism from L(X)  onto   L(X)/ F_0(X)   is generalized Drazin invertible?