Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9495964 | Journal of Functional Analysis | 2005 | 20 Pages |
Abstract
Suppose A is a dual Banach algebra, and a representation Ï:AâB(â2) is unital, weak* continuous, and contractive. We use a “Hilbert-Schmidt version” of Arveson distance formula to construct an operator space X, isometric to â2ââ2, such that the space of completely bounded maps on X consists of Hilbert-Schmidt perturbations of Ï(A)âIâ2. 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 K1(CB(X)) contains Z2 as a subgroup, and a completely indecomposable operator space containing an infinite dimensional homogeneous Hilbertian subspace.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Timur Oikhberg,