Perturbation theory of p-adic Fredholm and semi-Fredholm operators |
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Authors: | C Perez-Garcia S Vega |
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Affiliation: | a Dpto. de Matemáticas, Estadística y Computacíón, Facultad de Ciencias, Universidad de Cantabria, Avda. de los Castros, s/n 39071 Santander, Spain b Dpto. de Matemáticas, Ed. Tecnológico, Universidad de León, Campus Universitario de Vegazana, 24071 León, Spain |
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Abstract: | The main goal of this paper is to prove that Fredholm and semi-Fredholm operators between p-adic (or non-archimedean) Banach spaces, as well as the index of those that are Fredholm, are preserved when they are perturbed by a small operator. In this way we obtain the non-archimedean counterparts of some well-known results of classical Operator Theory. For non-spherically complete fields the classical techniques are no longer valid in the p-adic context, which forces us to seek a completely different way to attack the problem. The p-adic concept of orthogonality will be one of the key tools to get our purpose. |
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Keywords: | 47S10 46S10 |
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