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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