Injectivity of operator spaces

Ruan, Zhong-Jin

doi:10.1090/S0002-9947-1989-0929239-3

Injectivity of operator spaces
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Trans. Amer. Math. Soc. 315 (1989), 89-104 Request permission

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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