CONVEX TRACE FUNCTIONS OF SEVERAL VARIABLES ON C-ALGEBRAS

For each trace τ on a C*-algebra A generated by mutually commuting C*-subalgebras A1, A2,..., An and every convex function f of n variables we show that the function (x1, x2,..., xn) → τ(f(x1, x2,..., xn)) is convex on the space $\underset{\mathrm{k}=1}{\overset{\mathrm{n}}{\bigoplus }}\left(({\mathrm{A}}_{\mathrm{k}}{)}_{\mathrm{s}\mathrm{a}}\right)$.