Strictly singular operators on the Baernstein and Schreier spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909780410368000 |
|---|---|
| author | Laustsen, Niels Jakob JamesSmith |
| author_facet | Laustsen, Niels Jakob JamesSmith |
| contents | Every composition of two strictly singular operators is compact on the Baernstein space $B_p$ for $1 < p < \infty$ and on the $p$-convexified Schreier space $S_{p}$ for $1 \leq p < \infty$. Furthermore, every subsymmetric basic sequence in $B_p$ (respectively, $S_p$) is equivalent to the unit vector basis for $\ell_p$ (respectively, $c_0$), and the Banach spaces $B_p$ and $S_p$ contain block basic sequences whose closed span is not complemented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08796 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strictly singular operators on the Baernstein and Schreier spaces Laustsen, Niels Jakob JamesSmith Functional Analysis 46H10, 47L10 (primary) 46B03, 46B45, 47L20 (secondary) Every composition of two strictly singular operators is compact on the Baernstein space $B_p$ for $1 < p < \infty$ and on the $p$-convexified Schreier space $S_{p}$ for $1 \leq p < \infty$. Furthermore, every subsymmetric basic sequence in $B_p$ (respectively, $S_p$) is equivalent to the unit vector basis for $\ell_p$ (respectively, $c_0$), and the Banach spaces $B_p$ and $S_p$ contain block basic sequences whose closed span is not complemented. |
| title | Strictly singular operators on the Baernstein and Schreier spaces |
| topic | Functional Analysis 46H10, 47L10 (primary) 46B03, 46B45, 47L20 (secondary) |
| url | https://arxiv.org/abs/2509.08796 |