Representation of a completely bounded bimodule map

Na, Qi Yuan

doi:10.1090/S0002-9939-1995-1223518-9

Representation of a completely bounded bimodule map
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Proc. Amer. Math. Soc. 123 (1995), 1137-1143 Request permission

Abstract:

In this paper, we give a representation for a completely bounded $A - B$ bimodule map into $B(H)$, where A and B are unital operator subalgebras of $B(H)$. When A and B are ${C^ \ast }$-subalgebras we give a new proof of the Wittstock’s theorem by using this representation. We also prove that a von Neumann algebra is an injective operator bimodule over its unital operator algebras if and only if it is a finitely injective operator bimodule.

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