Operator log-convex functions and operator means

By T. Andô, Fumio Hiai. 2009

109 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1908aedf0a5a7f27ac1e5009be083b28ef53f4af

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In Applied Mathematics

1. Miklós Pálfia
2. Yongdo Lim
3. P. Denes
4. Fumio Hiai

In Computational Theory and Mathematics

1. Miklós Pálfia
2. P. Denes
3. Fumio Hiai
4. Yongdo Lim

Citations in the corpus

• Introduction to Matrix Analysis and Applications (2014, background): “1 in [8] is used to conclude that 1/f is operator monotone decreasing, so f is operator monotone.”
• Matrix power means and the Karcher mean (2012, background): “respectively; these follow from the equivalence between operator monotonicity and operator logconcavity by Ando and Hiai [1].”