A degree theory for locally compact perturbations of Fredholm maps in Banach spaces

摘要

We present an integer valued degree theory for locally compactperturbations of Fredholm maps of index zero between (open setsin) Banach spaces (quasi-Fredholm maps, for short). Theconstruction is based on the Brouwer degree theory and on thenotion of orientation for nonlinear Fredholm maps given by theauthors in some previous papers. The theory includes in a naturalway the celebrated Leray-Schauder degree.