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The Operator Space Projective Tensor Product: Embedding into the Second Dual and Ideal Structure

Published online by Cambridge University Press:  05 September 2013

Ranjana Jain  and
Ajay Kumar
Ranjana Jain
Affiliation:
Department off Mathematics, Lady Shri Ram College for Women, Lajpat Nagar IV, New Delhi 110024, India, (ranjanaj_81@rediffmail.com)
Ajay Kumar
Affiliation:
Department of Mathematics, University of Delhi, Delhi 110007, India, (akumar@maths.du.ac.in)
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Abstract

We prove that, for operator spaces V and W, the operator space V** ⊗hW** can be completely isometrically embedded into (V ⊗hW)**, ⊗h being the Haagerup tensor product. We also show that, for exact operator spaces V and W, a jointly completely bounded bilinear form on V × W can be extended uniquely to a separately w*-continuous jointly completely bounded bilinear form on V× W**. This paves the way to obtaining a canonical embedding of into with a continuous inverse, where is the operator space projective tensor product. Further, for C*-algebras A and B, we study the (closed) ideal structure of which, in particular, determines the lattice of closed ideals of completely.

Keywords

operator spaceC*-algebrasoperator space projective normHaagerup normPrimary 46L0646L0747L25
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 2 , June 2014 , pp. 505 - 519
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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