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arXiv · 2307.15315

Weak log-majorization and inequalities of power means

Miran Jeong·Sejong Kim
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Abstract

As non-commutative versions of the quasi-arithmetic mean, we consider the Lim-P\'{a}lfia's power mean, R\'{e}nyi right mean and R\'{e}nyi power means. We prove that the Lim-P\'{a}lfia's power mean of order $t \in [-1,0)$ is weakly log-majorized by the log-Euclidean mean and fulfills the Ando-Hiai inequality. We establish the log-majorization relationship between the R\'{e}nyi relative entropy and the product of square roots of given variables. Furthermore, we show the norm inequalities among power means and provide the boundedness of R\'{e}nyi power mean in terms of the quasi-arithmetic mean.

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Miran Jeong, Sejong Kim. 2023-07-28. Weak log-majorization and inequalities of power means. https://arxiv.org/abs/2307.15315

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