Authors: Ivković, Stefan 
Title: Semi-Fredholm theory on Hilbert C*-modules
Journal: Banach Journal of Mathematical Analysis
Volume: 13
Issue: 4
First page: 989
Last page: 1016
Issue Date: 9-Oct-2019
Rank: M22
ISSN: 1735-8787
DOI: 10.1215/17358787-2019-0022
We establish the semi-Fredholm theory on Hilbert C*-modules as a continuation of Fredholm theory on Hilbert C*-modules established by Mishchenko and Fomenko. We give a definition of a semi-Fredholm operator on Hilbert C*-module, and we prove that these semi-Fredholm operators are those that are one-sided invertible modulo compact operators, that the set of proper semi-Fredholm operators is open, and many other results that generalize their classical counterparts.
Keywords: (Semi-) Fredholm operators | index theories
Publisher: Tusi Mathematical Research Group

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