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

Keywords: $C^*$-algebra, trace function, Fr\'echet derivative, operator function

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