The standard dual of an operator space
type: Item
instance of: scholarly article
title: The standard dual of an operator space
zbMATH Open document ID: 0726.47030
author: David P. Blecher
published in: Pacific Journal of Mathematics
publication date: 1992-01-01T00:00:00Z
review text: If X is a linear space of operators on a Hilbert space, then it turns out that there is a natural, enlightening, nontrivial way to regard the dual \(X^*\) also as a linear space of operators on a (different) Hilbert space. The importance of this was pointed out in the work with \textit{V. I. Paulsen} [`Tensor products of operator spaces', J. Functional Anal., to appear], and also independently by Effros and Ruan. The purpose of this paper is to establish some fundamental properties of this construction, and to examine how it interacts with other natural categorical constructions with operator spaces. In the latter half of the paper we define and study a notion of projectivity (dual to injectivity) for operator spaces, and give a noncommutative version of Grothendieck's characterization of \(\ell^ 1(I)\) spaces for a discrete set I.
Mathematics Subject Classification ID: 47L50
Mathematics Subject Classification ID: 47L05
Mathematics Subject Classification ID: 46M10
zbMATH DE Number: 4198876
zbMATH Keywords: standard dual of an operator space
zbMATH Keywords: linear space of operators on a Hilbert space
zbMATH Keywords: projectivity
zbMATH Keywords: injectivity
zbMATH Keywords: noncommutative version of Grothendieck's characterization of \(\ell ^ 1(I)\) spaces for a discrete set I
MaRDI profile type: Publication
full work available at URL: pjm.1992.153.15
OpenAlex ID: W2037754914
DOI: 10.2140/PJM.1992.153.15
description: scientific article; zbMATH DE number 4198876