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$c^*$-algebras

Proceedings of the Edinburgh Mathematical Society (1)

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INVOLUTION AND THE HAAGERUP TENSOR PRODUCT
Ajay Kumar
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 44 / Issue 2 / June 2001

Published online by Cambridge University Press:

20 January 2009, pp. 317-322
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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