A norm inequality on noncommutative symmetric spaces related to a question of Bourin
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914754092597248 |
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| author | Liu, Jinchen He, Kan Zhao, Xingpeng |
| author_facet | Liu, Jinchen He, Kan Zhao, Xingpeng |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_09250 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A norm inequality on noncommutative symmetric spaces related to a question of Bourin Liu, Jinchen He, Kan Zhao, Xingpeng Functional Analysis 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. |
| title | A norm inequality on noncommutative symmetric spaces related to a question of Bourin |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2404.09250 |