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On Positive Definiteness Over Locally Compact Quantum Groups

Published online by Cambridge University Press:  20 November 2018

Volker Runde  and
Ami Viselter
Volker Runde
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada e-mail: vrunde@ualberta.ca
Ami Viselter
Affiliation:
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada e-mail: vrunde@ualberta.ca Department of Mathematics, University of Haifa, 31905 Haifa, Israel e-mail: aviselter@staff.haifa.ac.il
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Abstract

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The notion of positive-definite functions over locally compact quantum groups was recently introduced and studied by Daws and Salmi. Based on this work, we generalize various well-known results about positive-definite functions over groups to the quantum framework. Among these are theorems on “square roots” of positive-definite functions, comparison of various topologies, positive-definite measures and characterizations of amenability, and the separation property with respect to compact quantum subgroups.

Keywords

20G4222D2543A3546L5146L5246L89bicrossed productlocally compact quantum groupnon-commutative Lp -spacepositive-definite functionpositive-definite measureseparation property

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 68 , Issue 5 , 01 October 2016 , pp. 1067 - 1095
Copyright
Copyright © Canadian Mathematical Society 2016

References

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