Bi-extremity of embeddings of operator spaces into their injective envelopes

摘要

Abstract In this study of non-commutative convexity in the context of operator spaces, we explore extremal nature of embedding of an operator space in its injective envelope. We introduce the notions of bi-extremity of completely contractive (CC) maps on operator spaces and of prime TROs generated by them in the context of Hilbert C∗documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$C^*$$end{document}-bimodules. It is shown that if the generated TRO of an operator space is prime, then the CC embedding of the operator space in its injective envelope is bi-extreme.