Operator spaces with prescribed sets of completely bounded maps

摘要

Suppose A is a dual Banach algebra, and a representation pi : A -> B(l(2)) is unital, weak* continuous, and contractive. We use a "Hilbert-Schmidt version" of Arveson distance formula to construct an operator space X, isometric to l(2) circle times l(2), such that the space of completely bounded maps on X consists of Hilbert-Schmidt perturbations of pi(A) circle times I-l2. This allows us to establish the existence of operator spaces with various interesting properties. For instance, we construct an operator space X for which the group K-1(CB(X)) contains Z(2) as a subgroup, and a completely indecomposable operator space containing an infinite dimensional homogeneous Hilbertian subspace. (c) 2004 Elsevier Inc. All rights reserved.