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EVERY TOPOLOGICALLY AMENABLE LOCALLY COMPACT QUANTUM GROUP IS AMENABLE

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  15 May 2012

AMIN ZOBEIDI
AMIN ZOBEIDI*
Affiliation:
Department of Mathematics, Chamran University, Ahvaz, Iran (email: zobeidiamin@gmail.com)
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Abstract

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We prove that every topologically amenable locally compact quantum group is amenable. This answers an open problem by Bédos and Tuset [‘Amenability and co-amenability for locally compact quantum groups’, Internat. J. Math.14 (2003), 865–884].

Keywords

locally compact quantum groupamenability

MSC classification

Secondary: 46L89: Other “noncommutative” mathematics based on $C^*$-algebra theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 1 , February 2013 , pp. 149 - 151
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

References

[1]Bédos, E. and Tuset, L., ‘Amenability and co-amenability for locally compact quantum groups’, Internat. J. Math. 14 (2003), 865–884.CrossRefGoogle Scholar
[2]Desmedt, P., Quaegebeur, J. and Vaes, S., ‘Amenability and the bicrossed product construction’, Illinois J. Math. 46 (2002), 1259–1277.CrossRefGoogle Scholar
[3]Kustermans, J. and Vaes, S., ‘Locally compact quantum groups’, Ann. Sci. Éc. Norm. Supér. 33 (2000), 837–934.CrossRefGoogle Scholar
[4]Runde, V., ‘Uniform continuity over locally compact quantum groups’, J. Lond. Math. Soc. 80 (2009), 55–71.Google Scholar