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INVOLUTION AND THE HAAGERUP TENSOR PRODUCT

Published online by Cambridge University Press:  20 January 2009

Ajay Kumar
Ajay Kumar
Affiliation:
Department of Mathematics, Rajdhani College (University of Delhi), Raja Garden, New Delhi 110015, India ([email protected])
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Abstract

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We show that the involution $\theta(a\otimes b)=a^*\otimes b^*$ on the Haagerup tensor product $A\otimes_{\mrm{H}}B$ of $C^*$-algebras $A$ and $B$ is an isometry if and only if $A$ and $B$ are commutative. The involutive Banach algebra $A\otimes_{\mrm{H}}A$ arising from the involution $a\otimes b\to b^*\otimes a^*$ is also studied.

AMS 2000 Mathematics subject classification: Primary 46L05; 46M05

Keywords

$C^*$-algebrasHaagerup tensor productsecond dualclosed ideals
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 2 , June 2001 , pp. 317 - 322
Copyright
Copyright © Edinburgh Mathematical Society 2001