Year: 2020
Type: article
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.
Author: S. Ivković
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3011770943