Algebraic multiplicity and topological degree for Fredholm operators

Abstract

This paper tries to establish a link between topological and algebraic methods in nonlinear analysis showing how the topological degree for Fredholm operators of index zero of Fitzpatrick, Pejsachowicz and Rabier [11] can be determined from the generalized algebraic multiplicity of Esquinas and López-Gómez [8], [7], [22], in the same vein as the Leray–Schauder degree can be calculated from the Schauder formula through the classical algebraic multiplicity.