Averaging multipliers on locally compact quantum groups

Daws, Matthew and Krajczok, Jacek and Voigt, Christian (2025) Averaging multipliers on locally compact quantum groups. Journal of the London Mathematical Society, 111 (3): e70104. ISSN 0024-6107

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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.