On inner ideals in ternary algebras
type: Item
instance of: scholarly article
title: On inner ideals in ternary algebras
zbMATH Open document ID: 0676.46049
DOI: 10.1007/BF02570876
published in: Mathematische Zeitschrift
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/183773
review text: Let B be a weak* closed ternary subalgebra of a \(W^*\)-algebra A. If e and f are projections in A such that eBf is a subset of B then eBf is a \(weak^*\) closed inner ideal in B. In terms of the partial isometries in B, a condition is given for pairs (e,f) of projections in A to satisfy \(eBf\subseteq B\). It is shown that for every weak* closed inner ideal J in B there exists a pair (e,f) of projections in A satisfying this condition such that \(J=eBf\). As an application of the main result, a complete description of the weak* closed inner ideals in a continuous \(JBW^*\)-triple having a maximal faithful tripotent is given.
Mathematics Subject Classification ID: 46L70
Mathematics Subject Classification ID: 46L10
zbMATH DE Number: 4107478
zbMATH Keywords: weak\({}^ *\) closed ternary subalgebra of a \(W^ *\)-algebra
zbMATH Keywords: \(weak^ *\) closed inner ideals in a continuous \(JBW^ *\)-triple having a maximal faithful tripotent
author: C. M. Edwards
author: Gottfried T. Rüttimann
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4107478