Some Remarks on the Cone of Completely Positive Maps between Von Neumann Algebras |
| |
Authors: | Anantharaman-Delaroche C |
| |
Institution: | Université d'Orléans, Département de Mathématiques B.P. 6759, 45067 Orleans Cedex 2, France |
| |
Abstract: | The close relationship between the notions of positive formsand representations for a C*-algebra A is one of the most basicfacts in the subject. In particular the weak containment ofrepresentations is well understood in terms of positive forms:given a representation of A in a Hilbert space H and a positiveform on A, its associated representation is weakly containedin (that is, ker ker ) if and only if belongs to the weak*closure of the cone of all finite sums of coefficients of .Among the results on the subject, let us recall the followingones. Suppose that A is concretely represented in H. Then everypositive form on A is the weak* limit of forms of the typex ki=1 i, xi with the i in H; moreover if A is a von Neumannsubalgebra of (H) and is normal, there exists a sequence (i)i 1 in H such that (x) = i 1 i, xi for all x. |
| |
Keywords: | |
本文献已被 Oxford 等数据库收录! |
|