Geodesic
On non-adjointable semi-C*-Fredholm operators and semi-C*-Weyl operators
Filomat, Tome 37 (2023) no. 17, p. 5523

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DOI

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.
DOI : 10.2298/FIL2317523I
Classification : 47A53, 46L08
Keywords: Hilbert C*-module, Non-adjointable semi-C*-Fredholm operator, Semi-C*-Weyl operator, Fredholm alternative 
Stefan Ivković. On non-adjointable semi-C*-Fredholm operators and semi-C*-Weyl operators. Filomat, Tome 37 (2023) no. 17, p. 5523 . doi: 10.2298/FIL2317523I
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     title = {On non-adjointable {semi-C*-Fredholm} operators and {semi-C*-Weyl} operators},
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     year = {2023},
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     doi = {10.2298/FIL2317523I},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2317523I/}
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