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| In 2006, Benevieri and Furi presented a quite simple construction of a topological degree for compact perturbations of Fredholm maps of index zero between Banach spaces, called quasi-Fredholm maps.
This degree verifies the three fundamental properties of the classical degree theory: Normalization, Additivity and Homotopy invariance. We show here that this degree is unique. Precisely, by an axiomatic approach similar to the one due to Amann-Weiss, we prove that there exists at most one real function satisfying the above properties, and this function must be integer valued.
In addition, we show that the degree for quasi-Fredholm maps provides
in a natural way a generalization of the Leray-Schauder degree.
This is a joint work with Pierluigi Benevieri and Massimo Furi. |
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