Selfadjointness criteria for operator algebras
type: Item
instance of: scholarly article
title: Selfadjointness criteria for operator algebras
zbMATH Open document ID: 0978.47054
author: Christian Le Merdy
published in: Archiv der Mathematik
publication date: 2002-01-15T00:00:00Z
review text: Let \(A\) be a closed subalgebra of the algebra \(B(H)\) of all bounded linear operators on a Hilbert space \(H\). Assume that for every completely isometric representation \(\pi:A\to B(H)\), the commutant \((\pi(A))'\) is a selfadjoint. Then the author proves that \(A\) itself must be a selfadjoint algebra. If \(A\) is closed in the weak* topology of \(B(H)\), then one need only consider weak*-continuous completely isometric representations \(\pi\). The proofs use methods developed in the study of operator spaces.
reviewed by: H. Bercovici
Mathematics Subject Classification ID: 47L30
Mathematics Subject Classification ID: 46B28
zbMATH DE Number: 1449202
zbMATH Keywords: operator algebra
zbMATH Keywords: operator space
zbMATH Keywords: complete isometry
zbMATH Keywords: commutant
zbMATH Keywords: \(C^*\) algebra
zbMATH Keywords: selfadjointness
zbMATH Keywords: completely isometric representation
MaRDI profile type: Publication
full work available at URL: s000130050433
OpenAlex ID: W2134773278
DOI: 10.1007/S000130050433
description: scientific article; zbMATH DE number 1449202