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## Studia Mathematica

2003 | 154 | 2 | 137-164
Tytuł artykułu

### On completely bounded bimodule maps over W*-algebras

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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.
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Tom
Numer
Strony
137-164
Opis fizyczny
Daty
wydano
2003
Twórcy
autor
• Department of Mathematics, University of Ljubljana, Jadranska 19, Ljubljana 1000, Slovenia
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