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Two trace inequalities for operator functions

2019/04/02 by Dinh, Trung Hoa, Ho, Minh Toan, Le, Cong Trinh +1
#46L51 #47A30 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1904.01961

Abstract

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

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