A DEGREE THEORY FOR LOCALLY COMPACT PERTURBATIONS OF FREDHOLM MAPS IN BANACH SPA.

We present an integer valued degree theory for locally compact perturbations of Fredholm maps of index zero between (open sets in) Banach spaces (quasi-Fredholm maps, for short). The construction is based on the Brouwer degree theory and on the notion of orientation for nonlinear Fredholm maps given by the authors in some previous papers. The theory includes in a natural way the celebrated Leray-Schauder degree. [ABSTRACT FROM AUTHOR]