Authors: Ivković, Stefan 
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On Drazin invertible C* -operators and generalized C*-Weyl operators
Journal: Annals of Functional Analysis
Volume: 14
Issue: 2
First page: 36
Issue Date: 1-Apr-2023
Rank: ~M22
ISSN: 2008-8752
DOI: 10.1007/s43034-023-00258-0
Generalized Weyl operators on Hilbert spaces have been introduced and studied by Djordjević (Proc Am Math Soc, 130:81–ll4, 2001). In this paper, we provide a generalization of his result in the setting of C*-operators on Hilbert C*-modules by giving sufficient conditions under which the sum of a generalized C*-Weyl operator and a finitely generated C*-operator is a generalized C*-Weyl operator. Also, we obtain an extension of Djordjević’s results from the case of operators on Hilbert spaces to the case of operators on Banach spaces. Next, we consider semi-C*-B-Fredholm operators on Hilbert C*-modules and give sufficient conditions under which the composition of two mutually commuting semi-C*-B-Fredholm operators is a semi-C*-B-Fredholm operator, thus generalizing the result by Berkani regarding semi-B-Fredholm operators on Banach spaces. Finally, we consider Drazin invertible C*-operators, and we give necessary and sufficient conditions for two mutually commuting C*-operators to be Drazin invertible when their composition is Drazin invertible.
Keywords: Drazin invertible C -operator * | Generalized C -Weyl operator * | Hilbert C -module * | Semi-C -B-Fredholm operator *
Publisher: Springer Link

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