Local properties of ternary rings of operators and their linking \(C^{*}\)-algebras
type: Item
instance of: scholarly article
title: Local properties of ternary rings of operators and their linking \(C^{*}\)-algebras
zbMATH Open document ID: 1027.46068
author: Manmohan Kaur
author: Zhong-Jin Ruan
published in: Journal of Functional Analysis
publication date: 2003-03-26T00:00:00Z
review text: A ternary ring of operators between Hilbert spaces \(K\) and \(H\) is a norm closed subspace \(V\) of \(B(K, H)\), which is closed under the triple product \[ (x,y,z)\in V\times V\times V\mapsto xy^* z\in V. \] In the paper under review, it is proved that some local properties, such as nuclearity, exactness, and local reflexivity of ternary ring of operators are closely related to the local properties of their linking \(C^*\)-algebras. Haagerup's decomposition property for completely bounded maps and Pisier's \(\delta\)-norm are also naturally generalized to a ternary ring of operators. In the Appendix, it is shown that for each \(n> 2\), there exists an operator space which is \((n+1)\)-locally reflexive, and is only \(\lambda\)-locally reflexive for \(\lambda\geq{n\over\sqrt{n-1}}\).
reviewed by: Dumitrŭ Popa
Mathematics Subject Classification ID: 46L07
Mathematics Subject Classification ID: 47L25
zbMATH DE Number: 1888358
zbMATH Keywords: operator spaces
zbMATH Keywords: TROs
zbMATH Keywords: \(C^{*}\)-algebras
zbMATH Keywords: local theory
zbMATH Keywords: ternary ring of operators
zbMATH Keywords: nuclearity
zbMATH Keywords: exactness
zbMATH Keywords: local reflexivity
MaRDI profile type: Publication
full work available at URL: jfan.2002.3951
OpenAlex ID: W2035430470
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DOI: 10.1006/JFAN.2002.3951
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description: scientific article; zbMATH DE number 1888358