On positive definiteness over locally compact quantum groups

Abstract

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.

28 pages; v3: incorporated several changes, most at the referee's suggestion; to appear in the Canadian Journal of Mathematics

References in corpus (1)

• Completely positive definite functions and Bochner's theorem for locally compact quantum groups

Cited by in corpus (3)

• Convolution semigroups on locally compact quantum groups and noncommutative Dirichlet forms
• Around Property (T) for quantum groups
• Convolution semigroups on Rieffel deformations of locally compact quantum groups