On completely bounded bimodule maps over W*-algebras

• Autorzy: Bojan Magajna
• Języki publikacji: EN

Abstrakty

EN

It is proved that for a von Neumann algebra A ⊆ B(ℋ ) the subspace of normal maps is dense in the space of all completely bounded A-bimodule homomorphisms of B(ℋ ) in the point norm topology if and only if the same holds for the corresponding unit balls, which is the case if and only if A is atomic with no central summands of type $I_{∞,∞}$. Then a duality result for normal operator modules is presented and applied to the following problem. Given an operator space X and a von Neumann algebra A, is the map $q:A {⊗\limits^{eh}} X ⊗{\limits^{eh}} A → X {⊗\limits^{np}} A$, induced by q(a ⊗ x ⊗ b) = x ⊗ ab, from the extended Haagerup tensor product to the normal version of the Pisier delta tensor product a quotient map? We give a reformulation of this problem in terms of normal extension of some completely bounded maps and answer it affirmatively in the case A is of type I and X belongs to a certain class which includes all finite-dimensional operator spaces.

Kategorie tematyczne

• 46L07: Operator spaces and completely bounded maps
• 47L25: Operator spaces (= matricially normed spaces)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 154
• Numer: 2
• Strony: 137-164

Daty

wydano

2003

Twórcy

autor

Bojan Magajna

• Department of Mathematics, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia

Identyfikatory

DOI

10.4064/sm154-2-3