We investigate monotone operator functions of several variables under a trace
or a trace-like functional. In particular, we prove the inequality \tau(x_1...
x_n)\le\tau(y_1... y_n) for a trace \tau on a C^*-algebra and abelian n-tuples
(x_1,...,x_n)\le (y_1,...,y_n) of positive elements. We formulate and prove
Jensen's inequality for expectation values, and we study matrix functions of
several variables which are convex or monotone with respect to the weak
majorization for matrices
