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Operator spaces

$ X$, $ Y$ operator spaces
$ B(\H)$ aqlgebra of bounded linear operators on $ \H$
$ M_n(X)$ $ M_n \otimes X$ matrices with entries from $ X$ (algebraically)
$ M_1(X)$ first level of the operator space $ X$
$ \mathit{CB}(X,Y)$ the operator space of completely bounded mappings
$ \mathit{CB}(X,Y)_A$ the operator space of completely bounded right $ A$-module homomorphisms
$ \mathit{CB}(X \times Y; Z)$ the operator space of completely bounded bilinear mappings
$ \mathit{JCB}(X \times Y; Z)$ the operator space of jointly completely bounded bilinear mappings
$ \Vert\cdot\Vert _\mathrm{jcb}$ norm of a jointly completely bounded bilinear mapping
$ X_0$, $ Y_0$ operator subspace of the corresponding operator spaces
$ X^*$ dual of the operator space $ X$



Prof. Gerd Wittstock 2001-01-07