Abstract
We study operator log-convex functions on (0, ∞), and prove that a continuous nonnegative function on (0, ∞) 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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Ando, T., Hiai, F. Operator log-convex functions and operator means. Math. Ann. 350, 611–630 (2011). https://doi.org/10.1007/s00208-010-0577-4
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DOI: https://doi.org/10.1007/s00208-010-0577-4