Convergence of logarithmic trace inequalities via generalized Lie-Trotter formulae

被引：8

作者：

Furuta, T ^{[1
]}

机构：

[1] Tokyo Univ Sci, Fac Sci, Dept Math Informat Sci, Shinjuku Ku, Tokyo 1628601, Japan

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2005年 / 396卷

关键词：

generalized Lie-Trotter formula; log majorization; logarithmic trace inequality;

D O I：

10.1016/j.laa.2004.09.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We shall extend logarithmic trace inequalities shown by Bebiano et al. [N. Bebiano, R. Lemos, J. da Providencia, Inequalities for quantum relative entropy, preprint] and also by Hiai and Petz [The Golden-Thompson trace inequality is complemented, Linear Algebra Appl. 181 (1993) 153-185], by applying log majorization equivalent to an order preserving operator inequality. We shall generalize the Lie-Trotter formulae, which extend the original Lie-Trotter formula, and the alpha-mean variant of the original Lie-Trotter formula in Hiai-Petz [Linear Algebra Appl. 181 (1993) 153-185]. By using this generalized Lie-Trotter formulae, we shall consider the convergence of certain logarithmic trace inequalities, as some extensions of Bebiano et al. [N. Bebiano, R. Lemos, J. da Providencia, Inequalities for quantum relative entropy, preprint] and Hiai-Petz [The Golden-Thompson trace inequality is complemented, Linear Algebra Appl. 181 (1993) 153-185]. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：353 / 372

页数：20

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