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C*-convex sets and completely bounded bimodule homomorphisms

Published online by Cambridge University Press:  11 July 2007

B. Magajna
Department of Mathematics, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia (


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.

Research Article
Copyright © Royal Society of Edinburgh 2000

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