Fredholm-type operators and index

Abstract

While in [13] we studied classes of Fredholm-type operators defined by the homomorphism Π from L(X) onto the Calkin algebra C(X), X being a Banach space, we study in this paper two classes of Fredholm-type operators defined by the homomorphism π from L(X) onto the algebra C0(X)=L(X)/F0(X), where F0(X) is the ideal of finite rank operators in L(X). Then we define an index for Fredholm-type operators and we show that this new index satisfies similar properties as the usual Fredholm index.