Some extensions of the semi-C*-Fredholm theory

Abstract

In this paper we prove that the set of semi-C∗-Weyl operators on self-dual Hilbert W ∗-modules forms a semigroup under the multiplication. Next, we introduce a new concept of generalized Fredholm operators on an infinite dimensional Hilbert space and we show that the set of these operators is invariant under finite rank perturbations, as well as some other results generalizing their classical counterparts. Moreover, we consider closed range C∗-operators and obtain some of their properties. Finally, we provide concrete examples of semi-C∗-Weyl operators.