Authors: Ivković, Stefan 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On Operators with Closed Range and Semi-Fredholm Operators Over W*-Algebras
Journal: Russian Journal of Mathematical Physics
Volume: 27
Issue: 1
First page: 48
Last page: 60
Issue Date: 1-Jan-2020
Rank: M22
ISSN: 1061-9208
DOI: 10.1134/S1061920820010057
In this paper, we consider A-Fredholm and semi-A-Fredholm operators on Hilbert C*-modules over a W*-algebra A defined in [3] and [9]. Using the assumption that A is a W*-algebra (rather than an arbitrary C*-algebra), we obtain a generalization of Schechter—Lebow characterization of semi-Fredholm operators and a generalization of the “punctured neighborhood” theorem, as well as some other results generalizing their classical counterparts. We consider both adjointable and nonadjointable semi-Fredholm operators over W*-algebras. Moreover, we also work with general bounded adjointable operators with closed ranges over C*-algebras and prove a generalization of a Bouldin result for Hilbert spaces to Hilbert C*-modules.
Publisher: Springer Link

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