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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Injectivity of operator spaces
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by Zhong-Jin Ruan PDF
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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Additional Information
  • © Copyright 1989 American Mathematical Society
  • 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