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 wellknown 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.
Bibliographical notePublisher Copyright:
© Canadian Mathematical Society 2016.
- Bicrossed product
- Locally compact quantum group
- Non-commutative L-space
- Positive-definite function
- Positive-definite measure
- Separation property
ASJC Scopus subject areas
- Mathematics (all)