Strongly subadditive functions

2010/07/27 by Koenraad Audenaer, Audenaer, Koenraad, Fumio Hiai +3
Mathematics · #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1007.4626

openalex publication_date 2010/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f be a function defined on positive numbers. The subject is the trace inequality Tr f(A) + Tr f(P₂AP₂) ≤ Tr f(P₁₂AP₁₂) + \Tr f(P₂₃AP₂₃), where A is a positive operator, P₁,P₂,P₃ are orthogonal projections such that P₁+P₂+P₃=I, P₁₂=P₁+P₂ and P₂₃=P₂+P₃. There are several examples of functions f satisfying the inequality (called (SSA)) and the case of equality is described.

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