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arXiv · 1910.05888

Twisted Fourier(-Stieltjes) spaces and amenability

Hun Hee Lee·Xiao Xiong
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Abstract

The Fourier(-Stieltjes) algebras on locally compact groups are important commutative Banach algebras in abstract harmonic analysis. In this paper we introduce a generalization of the above two algebras via twisting with respect to 2-cocycles on the group. We also define and investigate basic properties of the associated multiplier spaces with respect to a pair of 2-cocycles. We finally prove a twisted version of the results of Nebbia, Fendler, Bo\.{z}ejko, Losert and Ruan characterizing amenability of the underlying locally compact group through comparison of the twisted Fourier-Stieltjes space with the associated multiplier spaces.

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Hun Hee Lee, Xiao Xiong. 2019-10-14. Twisted Fourier(-Stieltjes) spaces and amenability. https://arxiv.org/abs/1910.05888

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