2017/02/18 by Marzieh Forough, Forough, Marzieh
Mathematics · #FOS: Mathematics #Holomorphic and Operator Theory #Numerical methods in inverse problems #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics #math.OA
paper · pdf · doi:10.48550/arxiv.1702.05611
10 pages
arxiv created 2017/02/18 · openalex publication_date 2017/02/18 · arxiv updated 2017/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the stability of Fredholm property for regular operators on Hilbert C^*-modules under some certain perturbations. We treat this problem when perturbing operators are (relatively) bounded or relatively compact. We also consider the perturbations of regular Fredholm operators in terms of the gap metric. In particular, we prove that the space of all regular Fredholm operators on a Hilbert C^*-module E is open in the space of all regular operators on E with respect to the gap metric. As an application, we construct some continuous paths of selfadjoint regular Fredholm operators with respect to the gap metric.