Failure of almost uniformly convergence for noncommutative martingales
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916314804649984 |
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| author | Hong, Guixiang Ricard, Éric |
| author_facet | Hong, Guixiang Ricard, Éric |
| contents | In this paper, we provide a counterexample to show that in sharp contrast to the classical case, the almost uniform convergence may not happen for truly noncommutative $L_p$-martingales when $1\leq p<2$. The same happens to ergodic averages. The proof consists of some sharp estimates of the distributional function of a sequence of matrices and some non standard transference techniques, which might admit further applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08560 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Failure of almost uniformly convergence for noncommutative martingales Hong, Guixiang Ricard, Éric Operator Algebras Functional Analysis In this paper, we provide a counterexample to show that in sharp contrast to the classical case, the almost uniform convergence may not happen for truly noncommutative $L_p$-martingales when $1\leq p<2$. The same happens to ergodic averages. The proof consists of some sharp estimates of the distributional function of a sequence of matrices and some non standard transference techniques, which might admit further applications. |
| title | Failure of almost uniformly convergence for noncommutative martingales |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2402.08560 |