Operator log-convex functions and f-divergence functional

Mohsen Kian

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arXiv · 1305.7308

Operator log-convex functions and f-divergence functional

Mohsen Kian

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Abstract

We present a characterization of operator log-convex functions by using positive linear mappings. Moreover, we study the non-commutative f-divergence functional of operator log-convex functions. In particular, we prove that f is operator log-convex if and only if the non-commutative f-divergence functional is operator log-convex in its first variable and operator convex in its second variable.

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Mohsen Kian. 2014-08-25. Operator log-convex functions and f-divergence functional. https://arxiv.org/abs/1305.7308

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