The Fourier-Stieltjes algebra of a C*-dynamical system
Abstract
In analogy with the Fourier-Stieltjes algebra of a group, we associate to a unital discrete twisted C*-dynamical system a Banach algebra whose elements are coefficients of equivariants representations of the system. Building upon our previous work, we show that this Fourier-Stieltjes algebra embeds continuously in the Banach algebra of completely bounded multipliers of the (reduced or full) C*-crossed product of the system. We also introduce a notion of positive definiteness and prove a Gelfand-Raikov type theorem allowing us to describe the Fourier-Stieltjes algebra of a system in a more intrinsic way. After a study of some of its natural commutative subalgebras, we end with a characterization of the Fourier-Stieltjes algebra involving C*-correspondences over the (reduced or full) C*-crossed product.
Keywords
Cite
@article{arxiv.1510.03296,
title = {The Fourier-Stieltjes algebra of a C*-dynamical system},
author = {Erik Bédos and Roberto Conti},
journal= {arXiv preprint arXiv:1510.03296},
year = {2018}
}
Comments
46 pages. Minor revision. A few typos were corrected. The proof that amenability of a system implies its regularity has been streamlined. To appear in Internat. J. Math