Abstract
In this paper, we consider \({\mathcal A}\)-Fredholm and semi-\({\mathcal A}\)-Fredholm operators on Hilbert C*-modules over a W*-algebra \({\mathcal A}\) defined in [3] and [9]. Using the assumption that \({\mathcal A}\) 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.
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Acknowledgment
I am especially grateful to my research supervisor Professor Vladimir M. Manuilov for carefully reading my paper and for inspiring comments and suggestions that led to an improved presentation of the text. I am also grateful to Professor Dragan S. Djordjevic for suggesting the research topic of the paper and for introducing the relevant reference books to me.
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Ivković, S. On Operators with Closed Range and Semi-Fredholm Operators Over W*-Algebras. Russ. J. Math. Phys. 27, 48–60 (2020). https://doi.org/10.1134/S1061920820010057
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DOI: https://doi.org/10.1134/S1061920820010057