Authors: | Ivković, Stefan | Affiliations: | Mathematics Mathematical Institute of the Serbian Academy of Sciences and Arts |
Title: | On non-adjointable semi-C*-Fredholm operators and semi-C*-Weyl operators | Journal: | Filomat | Volume: | 37 | Issue: | 17 | First page: | 5523 | Last page: | 5539 | Issue Date: | 2023 | Rank: | ~M22 | ISSN: | 0354-5180 | DOI: | 10.2298/FIL2317523I | Abstract: | We extend the results from semi-Fredholm theory of adjointable, bounded C*-operators on the standard C*-module, presented in [3], to the case of general bounded C*-operators on arbitrary Hilbert C*-modules. Next, in the special case of the standard C*-module, we show that the set of those semi-C*-Fredholm operators that are not semi-C*-Weyl operators is open in the norm topology, and that the set of non-adjointable semi-C*-Weyl operators is invariant under perturbations by general compact operators. Moreover, we provide an extended Schechter characterization and a generalized Fredholm alternative in the case of adjointable C*-operators on the standard C*-module. Finally, we provide examples of semi-C*-Fredholm operators. |
Publisher: | Faculty of Sciences and Mathematics, University of Niš |
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