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arXiv · 1904.01961

Two trace inequalities for operator functions

Trung Hoa Dinh·Minh Toan Ho·Cong Trinh Le·Bich Khue Vo
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Abstract

In this paper we show that for a non-negative operator monotone function $f$ on $[0, \infty)$ such that $f(0)= 0$ and for any positive semidefinite matrices $A$ and $B$, $$ Tr((A-B)(f(A)-f(B))) \le Tr(|A-B|f(|A-B|)). $$ When the function $f$ is operator convex on $[0, \infty)$, the inequality is reversed.

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Trung Hoa Dinh, Minh Toan Ho, Cong Trinh Le, Bich Khue Vo. 2019-04-02. Two trace inequalities for operator functions. https://arxiv.org/abs/1904.01961

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