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Preservation of the Inndex of p-Adic Linear Operators Under Compact Perturbations

Published online by Cambridge University Press:  04 December 2007

J. ARAUJO ,
C. PEREZ-GARCIA  and
S. VEGA
J. ARAUJO
Affiliation:
Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, 39071 Santander, Spain e-mail: araujo@matesco.unican.es, perezmc@matesco.unican.es, vegas@matesco.unican.es
C. PEREZ-GARCIA
Affiliation:
Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, 39071 Santander, Spain e-mail: araujo@matesco.unican.es, perezmc@matesco.unican.es, vegas@matesco.unican.es
S. VEGA
Affiliation:
Departamento de Matemáticas, Estadística y Computación, Facultad de Ciencias, Universidad de Cantabria, 39071 Santander, Spain e-mail: araujo@matesco.unican.es, perezmc@matesco.unican.es, vegas@matesco.unican.es
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Abstract

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In this paper it is proved that the index of a Fredholm operator between $p$-adic Banach spaces is preserved under compact perturbations. A case of special interest is provided when the ground field is nonspherically complete. In this case the classical techniques are no longer valid and the relation between the kernels of a Fredholm operator and that of a small compact perturbation turn out to be in general much richer than in the complex context.

Keywords

Fredholm operatorindexp-adic.
Type
Research Article
Information
Compositio Mathematica , Volume 118 , Issue 3 , September 1999 , pp. 291 - 303
Copyright
© 1999 Kluwer Academic Publishers