Operator log-convex functions and operator means

Details Operator log-convex functions and operator means Operator log-convex functions and operator means

2009-11-27

arxiv.org/abs/0911.5267v4

Mathematics

Functional Analysis

20 pages

Scientific paper

We study operator log-convex functions on $(0,\infty)$, and prove that a
continuous nonnegative function on $(0,\infty)$ is operator log-convex if and
only if it is operator monotone decreasing. Several equivalent conditions
related to operator means are given for such functions. Operator log-concave
functions are also discussed.

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