Perturbation theory for generalized Fredholm operators. II

Abstract

If T is a bounded linear operator with generalized inverse S, i.e. T S T = T TST = T , we obtain conditions so that T − U T - U has a generalized inverse. When T is a Fredholm operator, the conditions become simply the requirement that I − U S I - US (or equivalently I − S U I - SU ) is a Fredholm operator. This result includes the classical perturbation theorems where U is required to have a small norm or to be compact.