Hostname: page-component-5d59c44645-mhl4m Total loading time: 0 Render date: 2024-02-25T05:53:59.448Z Has data issue: false hasContentIssue false

C*-convex sets and completely bounded bimodule homomorphisms

Published online by Cambridge University Press:  11 July 2007

B. Magajna
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia (Bojan.Magajna@fmf.uni-lj.si)

Abstract

If A and B are C*-algebras and X is an operator A, B-bimodule, then points of X can be separated from closed A, B-absolutely convex subsets of X by completely bounded A, B-bimodule homomorphisms from X into B(K), where K is a Hilbert space and the A, B-bimodule structure on B(K) is induced by a pair of representations π : AB(K) and σ : BB(K). If A and B are von Neumann algebras and X is a normal (not necessarily dual) operator A, B-bimodule, those A, B-absolutely convex subsets of X are characterized which can be separated from points of X as above, but with the additional requirement that the two representations π and σ are normal. This requires a new topology on X, which has appeared also in connection with some other questions concerning operator modules.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)