2023/02/07 by Vladimir Manuilov, Manuilov, Vladimir, Evgenij Troitsky +1
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2302.03760
openalex publication_date 2023/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study such Hilbert C*-modules over a C*-algebra A, that 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.