Erik Bédos: Positive definiteness and C*-dynamical systems

Abstract:  In a recent work with R. Conti (La Sapienza Univ., Rome), we have introduced a notion of positive definiteness for certain functions associated to a (unital, discrete) C*-dynamical system. We will sketch the proof of a Gelfand-Raikov type theorem for such functions and use it to construct complete positive maps on the full and the reduced C*-crossed products of the system. We will also explain how a natural definition of amenability for C*-dynamical systems emerges from our work.