Preservation of the index of p-adic linear operators under compact perturbations

被引：11

作者：

Araujo, J ^{[1
]}

Perez-Garcia, C ^{[1
]}

Vega, S ^{[1
]}

机构：

[1] Univ Cantabria, Fac Ciencias, Dept Matemat Estadistica & Computac, Santander 39071, Spain

来源：

COMPOSITIO MATHEMATICA | 1999年 / 118卷 / 03期

关键词：

Fredholm operator; index; p-adic;

D O I：

10.1023/A:1001561127279

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 In this case the classical techniques are no longer valid and the relation between the kernels of a Fredholm operator and that of a small compact perturbation turn out to be in general much richer than in the complex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.

引用

页码：291 / 303

页数：13

共 12 条

[1] [Anonymous], 1978, Non-Archimedean functional analysis
[2] Index theorem for p-adic differential equations .2.
Christol, G
Mebkhout, Z
[J]. ANNALS OF MATHEMATICS, 1997, 146 (02) : 345 - 410
[3] THEOREM OF THE INDEX OF P-ADIC DIFFERENTIAL-EQUATIONS .1.
CHRISTOL, G
MEBKHOUT, Z
[J]. ANNALES DE L INSTITUT FOURIER, 1993, 43 (05) : 1545 - 1574
[4] CHRISTOL G, THEOREME INDICE EQUA
[5] Day MM, 1973, Normed linear spaces, P27
[6] GRUSON L, 1966, B SOC MATH FR, V94, P67
[7] INDEX OF P-ADIC DIFFERENTIAL OPERATORS .1.
ROBBA, P
[J]. ANNALS OF MATHEMATICS, 1975, 101 (02) : 280 - 316
[8] Robba P., 1994, EQUATIONS DIFFERENTI
[9] Schikhof W. H., 1989, 8911 CATH U DEP MATH, P1
[10] Serre J.-P., 1962, PUBL MATH-PARIS, V12, P69

← 1 2 →