Convexity properties of Tr[(a*a)n] Original Research Article

In this paper, for any even positive integer p=2n, we consider the function Ep(a)=Tr[(a*a)n] defined on a C*-algebra image with a faithful trace image. We show that the quadratic form Q(Ep)a associated to the Hessian of Ep at image is non-negative and for p>2 we give a simple characterization of the null-space. Finally, we show that g(t)=Ep(a+t b) is at least as convex as tp uniformly with respect to b.