On a matrix trace inequality due to Ando, Hiai and Okubo

Lucijan Plevnik ()
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Lucijan Plevnik: Institute of Mathematics, Physics and Mechanics

Indian Journal of Pure and Applied Mathematics, 2016, vol. 47, issue 3, 491-500

Abstract: Abstract Ando et al. have proved that inequality $$\Re \mathfrak{e}trA^{p_1 } B^{q_1 \ldots } A^{p_k } B^{q_k } \leqslant trA^{p_1 + \ldots + p_k } B^{q_1 + \ldots + q_k }p$$ ℜ e t r A p 1 B q 1 … A p k B q k ⩽ t r A p 1 + … + p k B q 1 + … + q k is valid for all positive semidefinite matrices A,B and those nonnegative real numbers p 1, q 1,..., p k , q k which satisfy certain additional conditions. We give an example to show that this inequality is not valid for all collections of p 1, q 1,..., p k , q k ≥ 0. We also study related trace inequalities.

Keywords: Inequality; positive semidefinite matrix; log-convexity (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13226-016-0180-9

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