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arXiv · 2312.13626

Averaging multipliers on locally compact quantum groups

Matthew Daws·Jacek Krajczok·Christian Voigt
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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.

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Matthew Daws, Jacek Krajczok, Christian Voigt. 2023-12-21. Averaging multipliers on locally compact quantum groups. https://arxiv.org/abs/2312.13626

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