Averaging multipliers on locally compact quantum groups

2023/12/21 by Daws, Matthew, Krajczok, Jacek, Voigt, Christian
#22D55 #43A07 #43A30 #46L67 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2312.13626

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.

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