Invertibility of the operators on Hilbert spaces and ideals in \(C^*\)-algebras
type: Item
instance of: scholarly article
title: Invertibility of the operators on Hilbert spaces and ideals in \(C^*\)-algebras
DOI: 10.1134/S0001434622090036
published in: Mathematical Notes
publication date: 2022-10-25T00:00:00Z
review text: In the present paper, the author investigate invertibility of the operators on Hilbert spaces and Ideals in \(C^{\ast }\)-Algebras. Among interesting results, it was obtained a sufficient conditions for the positivity and invertibility of operators from \(\mathcal{B(H)},\) the \(\ast \)-algebra of all linear bounded operators on the Hilbert space \(\mathcal{H}.\) Also, for a von Neumann algebra \(\mathcal{A}\) it is proved that every arbitrary symmetry \(S\in \mathcal{A}\) is written as the product \(A^{-1}UA\) with a positive invertible \(A\) and a self-adjoint unitary \(U\) from \(\mathcal{A}\).
reviewed by: Elhadj Dahia
Mathematics Subject Classification ID: 47A05
Mathematics Subject Classification ID: 47A63
Mathematics Subject Classification ID: 46L10
zbMATH DE Number: 7606781
zbMATH Keywords: Hilbert space
zbMATH Keywords: linear operator
zbMATH Keywords: invertible operator
zbMATH Keywords: von Neumann algebra
zbMATH Keywords: \(C^*\)-algebra
zbMATH Keywords: weight
author: Airat Bikchentaev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7606781