Publication: Axiomatization of the degree of Fitzpatrick, Pejsachowicz and Rabier
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2022-12-21
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Springer Nature
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Abstract
In this paper, we prove an analogue of the uniqueness theorems of Führer [15] and Amann and Weiss [1] to cover the degree of Fredholm operators of index zero constructed by Fitzpatrick, Pejsachowicz and Rabier [13], whose range of applicability is substantially wider than for the most classical degrees of Brouwer [5] and Leray–Schauder [22]. A crucial step towards the axiomatization of this degree is provided by the generalized algebraic multiplicity of Esquinas and López-Gómez [8, 9, 25], χ, and the axiomatization theorem of Mora-Corral [28, 32]. The latest result facilitates the axiomatization of the parity of Fitzpatrick and Pejsachowicz [12], σ(⋅,[a,b]), which provides the key step for establishing the uniqueness of the degree for Fredholm maps.
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CRUE-CSIC (Acuerdos Transformativos 2021)