On real operator spaces
type: Item
instance of: scholarly article
title: On real operator spaces
zbMATH Open document ID: 1058.46037
author: Zhong-Jin Ruan
publication date: 2003-11-10T00:00:00Z
review text: This paper deals with real operator spaces. By definition, a real operator space is a (closed) subspace of \(B(H)\), the space of all bounded linear operators on a real Hilbert space. The author gives an abstract characterization of such spaces, similar to his famous theorem on the characterization of the usual (complex) operator spaces. He has transferred many notions and results in the complex case to the present real setting. These include injectivity, tensor products, and others. Concerning injectivity, the author shows that a real operator space is injective iff it is a finite direct sum of rectangular matrix spaces with entries in \(\mathbb R\), \(\mathbb C\) and \(\mathbb H\) (\(\mathbb H\) being the quaternion ring). He also obtains a representation theorem for completely bounded maps from a \(C^*\)-algebra into a \(B(H)\).
reviewed by: Quanhua Xu
Mathematics Subject Classification ID: 46L07
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 47L25
zbMATH DE Number: 2002321
zbMATH Keywords: operator space
zbMATH Keywords: operator system
zbMATH Keywords: \(C^*\)-algebra
MaRDI profile type: Publication
full work available at URL: s10114-003-0278-y
OpenAlex ID: W2322081039
cites work: Q4520854
cites work: Q4722624
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DOI: 10.1007/S10114-003-0278-Y
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 2002321