Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-23T05:52:15.902Z Has data issue: false hasContentIssue false
  • English
  • Français

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])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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