Authors: Ivković, Stefan 
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Semi-Fredholm theory in C∗ -algebras
Journal: Banach Journal of Mathematical Analysis
Volume: 17
Issue: 3
First page: 51
Issue Date: 2023
Rank: ~M22
ISSN: 2662-2033
DOI: 10.1007/s43037-023-00277-y
Kečkić and Lazović introduced an axiomatic approach to Fredholm theory by considering Fredholm type elements in a unital C∗ -algebra as a generalization of C∗ -Fredholm operators on the standard Hilbert C∗ -module introduced by Mishchenko and Fomenko and of Fredholm operators on a properly infinite von Neumann algebra introduced by Breuer. In this paper, we establish semi-Fredholm theory in unital C∗ -algebras as a continuation of the approach by Kečkić and Lazović. We introduce the notion of a semi-Fredholm type element and a semi-Weyl type element in a unital C∗ -algebra. We prove that the difference between the set of semi-Fredholm elements and the set of semi-Weyl elements is open in the norm topology, that the set of semi-Weyl elements is invariant under perturbations by finite type elements, and several other results generalizing their classical counterparts. Also, we illustrate applications of our results to the special case of properly infinite von Neumann algebras and we obtain a generalization of the punctured neighbourhood theorem in this setting.
Keywords: Finite-type element | Semi-Fredholm type element | Semi-Weyl type element | von Neumann algebra
Publisher: Birkhauser

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