English

Monotone trace functions of several variables

Operator Algebras 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/0606444,
  title  = {Monotone trace functions of several variables},
  author = {Frank Hansen},
  journal= {arXiv preprint arXiv:math/0606444},
  year   = {2007}
}