Duke Mathematical Journal

On injectivity and nuclearity for operator spaces

Edward G. Effros, Narutaka Ozawa, and Zhong-Jin Ruan

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Abstract

An injective operator space $V$ which is dual as a Banach space has the form $eR(1-e)$, where $R$ is an injective von Neumann algebra and where $e$ is a projection in $R$. This is used to show that an operator space $V$ is nuclear if and only if it is locally reflexive and $V^{\ast\ast}$ is injective. It is also shown that any exact operator space is locally reflexive.

Article information

Source
Duke Math. J. Volume 110, Number 3 (2001), 489-521.

Dates
First available in Project Euclid: 18 June 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1087574979

Digital Object Identifier
doi:10.1215/S0012-7094-01-11032-6

Mathematical Reviews number (MathSciNet)
MR1869114

Zentralblatt MATH identifier
1010.46060

Subjects
Primary: 46L07: Operator spaces and completely bounded maps [See also 47L25]
Secondary: 46L08: $C^*$-modules

Citation

Effros, Edward G.; Ozawa, Narutaka; Ruan, Zhong-Jin. On injectivity and nuclearity for operator spaces. Duke Math. J. 110 (2001), no. 3, 489--521. doi:10.1215/S0012-7094-01-11032-6. http://projecteuclid.org/euclid.dmj/1087574979.


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