A norm inequality on noncommutative symmetric spaces related to a question of Bourin

In this note, we study a question introduced by Bourin \cite{2009Matrix} and partially solve the question of Bourin. In fact, for t\in[0,\frac{1}{4}]\cup[\frac{3}{4},1], we show that |||x^{t}y^{1-t}+y^{t}x^{1-t}|||\leq|||x+y|||, where x,y\in\mathbb{M}_{n}(\mathbb{C})^+ and \||\cdot\|| is the unitari...

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Bibliographic Details
Published inarXiv.org
Main Authors Liu, Jinchen, He, Kan, Zhao, Xingpeng
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 14.04.2024
Subjects
Mathematics - Functional Analysis
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Summary:In this note, we study a question introduced by Bourin \cite{2009Matrix} and partially solve the question of Bourin. In fact, for t\in[0,\frac{1}{4}]\cup[\frac{3}{4},1], we show that |||x^{t}y^{1-t}+y^{t}x^{1-t}|||\leq|||x+y|||, where x,y\in\mathbb{M}_{n}(\mathbb{C})^+ and \||\cdot\|| is the unitarily invariant norm. Moreover, we prove that the above inequality holds on noncommutative fully symmetric spaces.
ISSN:2331-8422
DOI:10.48550/arxiv.2404.09250