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Operator modules

$ A_1$, $ A_2$ $ C^*$-algebras
$ M$, $ N$ von Neumann algebras
$ \mathrm{Aut}(M)$ the set of $ ^*$-automorphisms of $ M$
$ \mathit{CB}_{(A_1,A_2)}(X,Y)$ the operator space of completely bounded left $ A_1$- right $ A_2$-module homomorphisms between $ X$ and $ Y$
$ \mathit{CB}^\sigma_{(A_1,A_2)}(X,Y)$ the operator space of normal completely bounded left $ A_1$- right $ A_2$-module homomorphisms between $ X$ and $ Y$
$ \mathit{CB}^s_{(A_1,A_2)}(X,Y)$ the operator space of singular completely bounded left $ A_1$- right $ A_2$-module homomorphisms between $ X$ and $ Y$



Prof. Gerd Wittstock 2001-01-07