Abstract and Applied Analysis 
Volume 2006 (2006), Article ID 64764, 20 pages
doi:10.1155/AAA/2006/64764

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

Pierluigi Benevieri and Massimo Furi

 Dipartimento di Matematica Applicata “G. Sansone,” Via S. Marta 3, Firenze 50139, Italy
Received 16 December 2003; Accepted 21 January 2005

Abstract

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.