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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Representation of a completely bounded bimodule map

Author: Qi Yuan Na
Journal: Proc. Amer. Math. Soc. 123 (1995), 1137-1143
MSC: Primary 46L05; Secondary 46L10, 47D25
MathSciNet review: 1223518
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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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Additional Information

PII: S 0002-9939(1995)1223518-9
Keywords: Operator bimodules, representation, dilation, injectivity, finite injectivity, finitely generated operator bimodule
Article copyright: © Copyright 1995 American Mathematical Society