On maximal non-selfadjoint reflexive algebras associated with a double triangle lattice
type: Item
instance of: scholarly article
title: On maximal non-selfadjoint reflexive algebras associated with a double triangle lattice
zbMATH Open document ID: 1357.47088
author: Ai Ju Dong
author: Dong Wang
published in: Science China. Mathematics
publication date: 2016-01-13T00:00:00Z
review text: Let \(\mathcal H\) be a Hilbert space of dimension greater than two and let \(\mathcal B(\mathcal H)\) be the algebra of all bounded linear operators on \(\mathcal H\). Let \(\mathcal L\) be a lattice in \(\mathcal B(\mathcal H)\) and \(\mathrm{Alg }\mathcal L\) the lattice algebra. \(\mathcal L\) is called a double triangle lattice if \(\mathcal L=\{P_i:i=1,2,3\}\) if \(P_i\wedge P_j=0\) as well as \(P_i\vee P_j=I\) for any \(i\not=j\). The authors prove that, if the double triangle lattice \(\mathcal L\) generates a \(II_1\) factor von Neumann algebra, then the lattice algebra \(\mathrm{Alg }\mathcal L\) is maximal non-selfadjoint in the class of all weak operator topology closed subalgebras with the same diagonal subalgebra \(\mathrm{Alg }\mathcal L\cap \mathrm{Alg }\mathcal L^*\).
Mathematics Subject Classification ID: 47L35
Mathematics Subject Classification ID: 46L10
zbMATH DE Number: 6529700
zbMATH Keywords: reflexive operator algebra
zbMATH Keywords: double triangle lattice
zbMATH Keywords: von Neumann algebra
zbMATH Keywords: \(II_1\) factor
zbMATH Keywords: maximality
zbMATH Keywords: Kadison-Singer algebra
zbMATH Keywords: Kadison-Singer lattice
reviewed by: Guoxing Ji
MaRDI profile type: Publication
full work available at URL: s11425-015-5031-3
OpenAlex ID: W2171091009
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DOI: 10.1007/S11425-015-5031-3
description: scientific article; zbMATH DE number 6529700