Twisted Fourier(-Stieltjes) spaces and amenability
Operator Algebras
2025-08-13 v2 Functional Analysis
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.
Keywords
Cite
@article{arxiv.1910.05888,
title = {Twisted Fourier(-Stieltjes) spaces and amenability},
author = {Hun Hee Lee and Xiao Xiong},
journal= {arXiv preprint arXiv:1910.05888},
year = {2025}
}
Comments
32 pages, major updates to include the case of Borel measurable 2-cocycles