1999/09/07 by David P. Blecher, Vern I. Paulsen, Blecher, David P. +1
Mathematics · #46M10 #47D15 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.FA #math.OA #msc:46M10 #msc:47D15
paper · pdf · doi:10.48550/arxiv.math/9909041
Revised version, January 21 2000
openalex publication_date 1999/09/07 · arxiv created 2000/01/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the injective envelope I(X) of an operator space X, showing amongst other things that it is a self-dual C^*-module. We describe the diagonal corners of the injective envelope of the canonical operator system associated with X. We prove that if X is an operator A-B-bimodule, then A and B can be represented completely contractively as subalgebras of these corners. Thus, the operator algebras that can act on X are determined by these corners of I(X) and consequently bimodules actions on X extend naturally to actions on I(X). These results give another characterization of the multiplier algebra of an operator space, which was introduced by the first author, and a short proof of a recent characterization of operator modules, and a related result. As another application, we extend Wittstock's module map extension theorem, by showing that an operator A-B-bimodule is injective as an operator A-B-bimodule if and only if it is injective as an operator space.