Complexifications of real operator spaces
type: Item
instance of: scholarly article
title: Complexifications of real operator spaces
zbMATH Open document ID: 1055.46040
author: Zhong-Jin Ruan
published in: Illinois Journal of Mathematics
publication date: 2004-01-19T00:00:00Z
review text: This paper is a continuation of the author's previous work on real operator spaces [Acta Math. Sin. Engl. Ser. 19, 485-496 (2003; Zbl 1058.46037)]. The main result of the present paper is the following interesting theorem on the complexification of real operator spaces. Theorem. Let \(V\) be a real operator space and \(V_c\) its algebraic complexification. Then there is unique complex operator space structure on \(V_c\) which extends the original real operator space structure on \(V\) and such that the natural conjugation on \(V_c\) is completely isometric. This theorem is powerful in the sense that it reduces problems on real operator spaces to the corresponding ones on their complexifications. For instance, \(V\) is injective, nuclear or exact if and only if \(V_c\), equipped with the structure above, is injective, nuclear or exact, respectively.
reviewed by: Quanhua Xu
Mathematics Subject Classification ID: 46L07
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 2028858
zbMATH Keywords: real operator space
zbMATH Keywords: complexification
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2028858