Real ideals of compact operators of complex factors
type: Item
instance of: scholarly article
title: Real ideals of compact operators of complex factors
zbMATH Open document ID: 1311.46053
author: Rashidkhon A. Dadakhodjaev
author: A. A. Rakhimov
author: S. Albeverio
published in: Positivity
publication date: 2014-09-24T00:00:00Z
review text: Let \(M\) be a \(W^*\)-algebra. A real subspace \(I\) of \(M\) is called a real ideal of \(M\) if \(I\cdot M\subset I+iI\). In the present paper, the authors investigate the real ideal of compact operators in complex \(W^*\)-algebras and give a description (up to isomorphisms) of real two-sided ideals in complex \(W^*\)-factors. In particular, they obtain real analogues of Halpern-Kaftal's theorem [\textit{H. Halpern} and \textit{V. Kaftal}, Math. Ann. 273, 251--270 (1986; Zbl 0591.46053)]. A concept of relative weak \((RW)_r\) convergence in a real Hilbert space is introduced. The classical Hilbert characterization of compactness of operators is extended to the compact operators in semi-finite real \(W^*\)-algebras.
Mathematics Subject Classification ID: 46L10
Mathematics Subject Classification ID: 46L37
zbMATH DE Number: 6347426
zbMATH Keywords: \(W^*\)-algebra
zbMATH Keywords: real factor
zbMATH Keywords: compact operator
zbMATH Keywords: real ideal
Wikidata QID: Q59394877
reviewed by: Sh. A. Ayupov
MaRDI profile type: Publication
full work available at URL: s11117-013-0226-8
OpenAlex ID: W2022867601
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DOI: 10.1007/S11117-013-0226-8
description: scientific article; zbMATH DE number 6347426