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On the Duality of Operator Spaces

Published online by Cambridge University Press:  20 November 2018

Christian Le Merdy
Christian Le Merdy*
Affiliation:
Equipe de Mathématiques, URA CNRS 741, Université de Franche-Comté, F-25030 Besançon Cedex, France
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Abstract

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We prove that given an operator space structure on a dual Banach space Y*, it is not necessarily the dual one of some operator space structure on Y. This allows us to show that Sakai's theorem providing the identification between C*-algebras having a predual and von Neumann algebras does not extend to the category of operator spaces. We also include a related result about completely bounded operators from B(ℓ2)* into the operator Hilbert space OH.

Keywords

47C1546A2046B28
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 3 , 01 September 1995 , pp. 334 - 346
Copyright
Copyright © Canadian Mathematical Society 1995

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