Monotone trace functions of several variables
Abstract
Description
We investigate monotone operator functions of several variables under a trace or a trace-like functional. In particular, we prove the inequality τ(x_1... x_n)\leτ(y_1... y_n) for a trace τon 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.