Strengthened convexity of positive operator monotone decreasing functions

Abstract

We prove a strengthened form of convexity for operator monotone decreasing positive functions defined on the positive real numbers. This extends Ando and Hiai's work to allow arbitrary positive maps instead of states (or the identity map), and functional calculus by operator monotone functions defined on the positive real numbers instead of the logarithmic function.

v3: correct typo (after publication), v2: minor changes, to appear in Math. Scand., v1: 5 pages

References in corpus (1)

• Operator log-convex functions and operator means

Cited by in corpus (1)

• Jointly convex mappings related to the Lieb's functional and Minkowski type operator inequalities