Erik Bédos: On the Fourier-Stieltjes algebra of a C*-dynamical system

Erik Bédos will give a talk with title: On the Fourier-Stieltjes algebra of a C*-dynamical system

Abstract: When G is a discrete group, its Fourier-Stieltjes algebra B(G) may be described as the set of coefficient functions associated with unitary representations of G on Hilbert spaces. In a similar way, if Sigma=(A, G, alpha, sigma) is a unital discrete twisted C*-dynamical system, one may let the Fourier-Stieltjes algebra B(Sigma) consist of the functions from G x A into A that arise as coefficient functions of equivariant representations of Sigma on Hilbert A-modules. We will explain how B(Sigma) may be organized as an algebra with conjugation, and show that it may be represented as completely bounded multipliers on the full crossed product C*(Sigma). (This is also known to be true for the reduced crossed product). This is part of an ongoing project with Roberto Conti (Rome).