Generalized B-Fredholm Banach algebra elements

摘要

Given a (not necessarily continuous) homomorphism between Banach algebras T:A -> B, an element a is an element of A will be said to be B-Fredholm (respectively, generalized B-Fredholm) relative to T, if T(a) is an element of B is Drazin invertible (respectively, Koliha-Drazin invertible). In this article, the aforementioned elements will be characterized and their main properties will be studied. In addition, perturbation properties will be also considered.