Averaging multipliers on locally compact quantum groups
Abstract
We study an averaging procedure for completely bounded multipliers on a locally compact quantum group with respect to a compact quantum subgroup. As a consequence we show that central approximation properties of discrete quantum groups are equivalent to the corresponding approximation properties of their Drinfeld doubles. This is complemented by a discussion of the averaging of Fourier algebra elements. We compare the biinvariant Fourier algebra of the Drinfeld double of a discrete quantum group with the central Fourier algebra. In the unimodular case these are naturally identified, but we show by exhibiting a family of counter-examples that they differ in general.
Cite
@article{arxiv.2312.13626,
title = {Averaging multipliers on locally compact quantum groups},
author = {Matthew Daws and Jacek Krajczok and Christian Voigt},
journal= {arXiv preprint arXiv:2312.13626},
year = {2024}
}
Comments
39 pages. Revision, correcting an error in Proposition 8.5 of the first version which affects some statements in section 8, and adding some further material