Journal of Operator Theory

Volume 50, Issue 1, Summer 2003 pp. 157-167.

Convex trace functions of several variables on

$C^*$ -algebras

Authors: Gert K. Pedersen
Author institution: Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark

Summary: For each trace

$\tau$ on a

$C^*$ -algebra

$A$ generated by mutually commuting

$C^*$ -subalgebras

$A_1,A_2, \ldots, A_n$ and every convex function

$f$ of

$n$ variables we show that the function

$(x_1, x_2, \ldots , x_n) \to \tau (f(x_1, x_2, \ldots , x_n))$ is convex on the space

$\bigoplus\limits_{k=1}^{ n} ((A_k)_{\sa})$ .

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