The Fourier-Stieltjes algebra of a C*-dynamical system

Erik Bédos; Roberto Conti

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arXiv · 1510.03296

The Fourier-Stieltjes algebra of a C*-dynamical system

Erik Bédos·Roberto Conti

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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.

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Erik Bédos, Roberto Conti. 2015-10-12. The Fourier-Stieltjes algebra of a C*-dynamical system. https://arxiv.org/abs/1510.03296

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