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.
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页数：12
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