Guardat en:
| Autors principals: | , |
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| Format: | Preprint |
| Publicat: |
2024
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| Matèries: | |
| Accés en línia: | https://arxiv.org/abs/2402.08045 |
| Etiquetes: |
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Taula de continguts:
- This is a continuation of our recent paper. We continue studying properties of the triangular projection ${\mathscr P}_n$ on the space of $n\times n$ matrices. We establish sharp estimates for the $p$-norms of ${\mathscr P}_n$ as an operator on the Schatten--von Neumann class $\boldsymbol{S}_p$ for $0<p<1$. Our estimates are uniform in $n$ and $p$ as soon as $p$ is separated away from 0. The main result of the paper shows that for $p\in(0,1)$, the $p$-norms of ${\mathscr P}_n$ on $\boldsymbol{S}_p$ behave as $n\to\infty$ and $p\to1$ as $n^{1/p-1}\min\big\{(1-p)^{-1},\log n\big\}$.