Hilbert C-Modules with Hilbert Dual and C-Fredholm Operators

被引：0

作者：

Manuilov, Vladimir ^{[1
]}

Troitsky, Evgenij ^{[1
]}

机构：

[1] Lomonosov Moscow State Univ, Moscow Ctr Fundamental & Appl Math, Dept Mech & Math, Moscow 119991, Russia

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2023年 / 95卷 / 03期

基金：

俄罗斯科学基金会;

关键词：

Hilbert C*-module; Monotone complete C*-algebra; Dual module; Self-dual module; Orthogonal complement; Polar decomposi-tion; A-Fredholm operator;

D O I：

10.1007/s00020-023-02737-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study Hilbert C*-modules over a C*-algebra A for which the Banach A-dual module carries a natural structure of Hilbert A module. In this direction we prove that if A is monotone complete, M and N are Hilbert A-modules, M is self-dual, and both T : M? N and its Banach A-dual T' : N'? M' have trivial kernels and cokernels then M ? N'. With the help of this result, for a monotone complete C*-algebra A, we prove that the index of any A-Fredholm operator can be calculated as the difference of its kernel and cokernel as in the Hilbert space case.

引用

页数：12

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Hilbert C*-Modules with Hilbert Dual and C*-Fredholm Operators

Hilbert C-Modules with Hilbert Dual and C-Fredholm Operators