Axiomatization of the degree of Fitzpatrick, Pejsachowicz and Rabier
| Autor: | Julián López-Gómez, Juan Carlos Sampedro |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | E-Prints Complutense. Archivo Institucional de la UCM instname |
| DOI: | 10.48550/arxiv.2106.11431 |
| Popis: | 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], $$\chi $$ χ , and the axiomatization theorem of Mora-Corral [28, 32]. The latest result facilitates the axiomatization of the parity of Fitzpatrick and Pejsachowicz [12], $$\sigma (\cdot ,[a,b])$$ σ ( · , [ a , b ] ) , which provides the key step for establishing the uniqueness of the degree for Fredholm maps. |
| Databáze: | OpenAIRE |
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