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 Norms for Schur products Commun. Korean Math. Soc. 1997 Vol. 12, No. 3, 571-577 Dong-Yun Shin Seoul City University Abstract : We first show that if $\psi{}:{}M_n(B(H))\rightarrow M_n(B(H))$ is a $D_n \otimes F(H)$-bimodule map, then there is a matrix $A \in M_n$ such that $\psi{}={}S_A.$ Secondly, we show that for an operator space $\Cal E,$ $A\in M_n,$ the Schur product map $S_A{}:{} M_n( \Cal E) \rightarrow M_n(\Cal E)$ and $\phi_A : M_n(\Cal E )\rightarrow \Cal E ,$ defined by $\phi_A ([x_{ij}])=\sum _{i,j=1} ^n a_{ij}x_{ij},$ we have $\Vert S_A \Vert {}={}\Vert S_A \Vert_{cb}{}={}\Vert A \Vert _S,$ $\Vert \phi_A \Vert {}={}\Vert \phi_A \Vert_{cb}{}={}\Vert A \Vert _1$ and obtain some characterizations of $A$ for which $S_A$ is contractive. Keywords : Operator Space, Operator System, Schur Product Map MSC numbers : 46L05 Downloads: Full-text PDF

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