On noncommutative Hölder inequality of Sukochev and Zanin for weak Schatten class
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916179403079680 |
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| author | Huang, Yi C. Luo, Sijie |
| author_facet | Huang, Yi C. Luo, Sijie |
| contents | Sukochev and Zanin resolved an open problem due to B. Simon concerning optimal constants in Hölder inequality for the weak Schatten classes of compact operators. In this note we observe that these constants, by introducing the modified weak Schatten quasi-norms, can be renormalised so that the original Simon's conjecture (with optimal constant 1) does hold. We also provide an unexpectedly simple proof for the modified Hölder inequality and its sharpness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17990 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On noncommutative Hölder inequality of Sukochev and Zanin for weak Schatten class Huang, Yi C. Luo, Sijie Functional Analysis Primary 46L52. Secondary 46E30 Sukochev and Zanin resolved an open problem due to B. Simon concerning optimal constants in Hölder inequality for the weak Schatten classes of compact operators. In this note we observe that these constants, by introducing the modified weak Schatten quasi-norms, can be renormalised so that the original Simon's conjecture (with optimal constant 1) does hold. We also provide an unexpectedly simple proof for the modified Hölder inequality and its sharpness. |
| title | On noncommutative Hölder inequality of Sukochev and Zanin for weak Schatten class |
| topic | Functional Analysis Primary 46L52. Secondary 46E30 |
| url | https://arxiv.org/abs/2403.17990 |