On positive definiteness over locally compact quantum groups (Q2828379)
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scientific article; zbMATH DE number 6643165
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On positive definiteness over locally compact quantum groups |
scientific article; zbMATH DE number 6643165 |
Statements
25 October 2016
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bicrossed product
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locally compact quantum group
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non-commutative \(L^p\)-space
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positive-definite function
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positive-definite measure
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separation property
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On positive definiteness over locally compact quantum groups (English)
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The purpose of this paper is to extend various properties of positive-definite functions from groups to quantum groups. The authors start from the notions of positive definiteness on locally compact quantum groups introduced in [\textit{M. Daws}, Int. J. Math. 23, No. 12, Paper No. 1250132, 23 p. (2012; Zbl 1282.43002)] and [\textit{M. Daws} and \textit{P. Salmi}, J. Funct. Anal. 264, No. 7, 1525--1546 (2013; Zbl 1320.46056)] and prove in the settings of locally compact quantum groups exciting results. ``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.''
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