On the degree for oriented quasi-Fredholm maps: its uniqueness and its effective extension of the Leray-Schauder degree

Pierluigi Benevieri, Alessandro Calamai, Massimo Furi

DOI: http://dx.doi.org/10.12775/TMNA.2015.052


In a previous paper, the first and third author developed a~degree theory for oriented locally compact perturbations of $C\sp{1}$ Fredholm maps of index zero between real Banach spaces. In the spirit of a celebrated Amann--Weiss paper, we prove that this degree is unique if it is assumed to satisfy three axioms: Normalization, Additivity and Homotopy invariance. Taking into account that any compact vector field has a canonical orientation, from our uniqueness result we shall deduce that the above degree provides an effective extension of the Leray--Schauder degree.


Topological degree, nonlinear Fredholm maps, Banach spaces, compact maps

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