On a matrix trace inequality due to Ando, Hiai and Okubo
On a matrix trace inequality due to Ando, Hiai and Okubo
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关于 Ando、Hiai 和 Okubo 的矩阵迹不等式
DOI：
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发表时间：
2016
影响因子：
0.7
通讯作者：
Lucijan Plevnik
中科院分区：
文献类型：
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作者：
Lucijan Plevnik
Ando et al. have proved that inequality ℜetrAp1Bq1…ApkBqk⩽trAp1+…+pkBq1+…+qkdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$Re mathfrak{e}trA^{p_1 } B^{q_1 ldots } A^{p_k } B^{q_k } leqslant trA^{p_1 + ldots + p_k } B^{q_1 + ldots + q_k }p$$end{document} is valid for all positive semidefinite matrices A,B and those nonnegative real numbers p1, q1,..., pk, qk which satisfy certain additional conditions. We give an example to show that this inequality is not valid for all collections of p1, q1,..., pk, qk ≥ 0. We also study related trace inequalities.
Ando et al. have proved that inequality ℜetrAp1Bq1…ApkBqk⩽trAp1+…+pkBq1+…+qkdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$Re mathfrak{e}trA^{p_1 } B^{q_1 ldots } A^{p_k } B^{q_k } leqslant trA^{p_1 + ldots + p_k } B^{q_1 + ldots + q_k }p$$end{document} is valid for all positive semidefinite matrices A,B and those nonnegative real numbers p1, q1,..., pk, qk which satisfy certain additional conditions. We give an example to show that this inequality is not valid for all collections of p1, q1,..., pk, qk ≥ 0. We also study related trace inequalities.