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Injectivity of operator spaces


Author: Zhong-Jin Ruan
Journal: Trans. Amer. Math. Soc. 315 (1989), 89-104
MSC: Primary 46L05; Secondary 47D15
DOI: https://doi.org/10.1090/S0002-9947-1989-0929239-3
MathSciNet review: 929239
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Abstract: We study the structure of injective operator spaces and the existence and uniqueness of the injective envelopes of operator spaces. We give an easy example of an injective operator space which is not completely isometric to any $ {C^\ast }$-algebra. This answers a question of Wittstock [23]. Furthermore, we show that an operator space $ E$ is injective if and only if there exists an injective $ {C^\ast }$-algebra $ A$ and two projections $ p$ and $ q$ in $ A$ such that $ E$ is completely isometric to $ pAq$.


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DOI: https://doi.org/10.1090/S0002-9947-1989-0929239-3
Article copyright: © Copyright 1989 American Mathematical Society

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