\(C^*\)-module algebras
type: Item
instance of: scholarly article
title: \(C^*\)-module algebras
zbMATH Open document ID: 1483.46060
author: Mohammad B. Asadi
author: Reza Rezavand
published in: Bulletin of the Iranian Mathematical Society
publication date: 2021-08-02T00:00:00Z
review text: The authors introduce the notion of a \(C^*\)-module algebra as an algebra \(E_0\) with involution which is a (two sided) module over a \(C^*\)-algebra \(\mathcal{A}\). They also prove that \(E_b\), the set of bounded elements of the completion \(E\) of \(E_0\), is a Banach \(*\)-algebra. They state the following notion. Let \(\mathcal{A}\) be a von Neumann algebra, a \(C^*\)-module algebra \(E\) over \(\mathcal{A}\) is called a \(W^*\)-module algebra if \(E\) has a predual as a Banach space. They prove that, if \(E_0\) is a symmetric pre \(C^*\)-module algebra over a von Neumann algebra \(\mathcal{A}\), then \(E_0'\) (the set of all bounded two sided \(\mathcal{A}\)-module maps from \(E_0\) to \(\mathcal{A}\)) is a \(W^*\)-module algebra.
reviewed by: Maryam Amyari
Mathematics Subject Classification ID: 46L08
Mathematics Subject Classification ID: 46K15
zbMATH DE Number: 7377344
zbMATH Keywords: Hilbert algebra
zbMATH Keywords: Hilbert \(C^*\)-module
zbMATH Keywords: \(C^*\)-module
zbMATH Keywords: \(W^*\)-module algebra
MaRDI profile type: Publication
full work available at URL: s41980-020-00422-5
OpenAlex ID: W3037840706
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DOI: 10.1007/S41980-020-00422-5
description: scientific article; zbMATH DE number 7377344