Twisted Fourier(-Stieltjes) spaces and amenability
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866909732768317440 |
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| author | Lee, Hun Hee Xiong, Xiao |
| author_facet | Lee, Hun Hee Xiong, Xiao |
| contents | 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, Bożejko, Losert and Ruan characterizing amenability of the underlying locally compact group through comparison of the twisted Fourier-Stieltjes space with the associated multiplier spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1910_05888 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Twisted Fourier(-Stieltjes) spaces and amenability Lee, Hun Hee Xiong, Xiao Operator Algebras Functional Analysis 43A30 (Primary), 46L07 (Secondary) 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, Bożejko, Losert and Ruan characterizing amenability of the underlying locally compact group through comparison of the twisted Fourier-Stieltjes space with the associated multiplier spaces. |
| title | Twisted Fourier(-Stieltjes) spaces and amenability |
| topic | Operator Algebras Functional Analysis 43A30 (Primary), 46L07 (Secondary) |
| url | https://arxiv.org/abs/1910.05888 |