Monotone trace functions of several variables

Details Monotone trace functions of several variables Monotone trace functions of several variables

2006-06-19

arxiv.org/abs/math/0606444v1

International Journal of Mathematics 16 (2005), 777-785

Mathematics

Operator Algebras

Scientific paper

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.

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