Abstract
Ando et al. have proved that inequality \(\Re \mathfrak{e}trA^{p_1 } B^{q_1 \ldots } A^{p_k } B^{q_k } \leqslant trA^{p_1 + \ldots + p_k } B^{q_1 + \ldots + q_k }p\) 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.
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Plevnik, L. On a matrix trace inequality due to Ando, Hiai and Okubo. Indian J Pure Appl Math 47, 491–500 (2016). https://doi.org/10.1007/s13226-016-0180-9
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DOI: https://doi.org/10.1007/s13226-016-0180-9