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Compact Operators in Regular LCQ Groups

Published online by Cambridge University Press:  20 November 2018

Mehrdad Kalantar
Mehrdad Kalantar*
Affiliation:
School of Mathematics and Statistics, Carleton University, Ottawa, ON e-mail: mkalanta@math.carleton.ca
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Abstract

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We show that a regular locally compact quantum group $\mathbb{G}$ is discrete if and only if ${{\mathcal{L}}^{\infty }}\left( \mathbb{G} \right)$ contains non-zero compact operators on ${{\mathcal{L}}^{2}}\left( \mathbb{G} \right)$ . As a corollary we classify all discrete quantum groups among regular locally compact quantum groups $\mathbb{G}$ where ${{\mathcal{L}}^{1}}\left( \mathbb{G} \right)$ has the Radon-Nikodym property.

Keywords

46L89locally compact quantum groupsregularitycompact operators

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 3 , 01 September 2014 , pp. 546 - 550
Copyright
Copyright © Canadian Mathematical Society 2014

References

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