| Autor: |
Wirzenius, Henrik |
| Rok vydání: |
2022 |
| Předmět: |
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| Zdroj: |
Mathematische Nachrichten 296 (2023), 4835-4853 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1002/mana.202200084 |
| Popis: |
We establish new results on the $\mathcal I$-approximation property for the Banach operator ideal $\mathcal I=\mathcal{K}_{up}$ of the unconditionally $p$-compact operators in the case of $1\le p<2$. As a consequence of our results, we provide a negative answer for the case $p=1$ of a problem posed by J.M. Kim (2017). Namely, the $\mathcal K_{u1}$-approximation property implies neither the $\mathcal{SK}_1$-approximation property nor the (classical) approximation property; and the $\mathcal{SK}_1$-approximation property implies neither the $\mathcal{K}_{u1}$-approximation property nor the approximation property. Here $\mathcal{SK}_p$ denotes the $p$-compact operators of Sinha and Karn for $p\ge 1$. We also show for all $2Comment: 23 pages |
| Databáze: |
arXiv |
| Externí odkaz: |
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