Quantification of Banach-Saks properties of higher orders
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911974811500544 |
|---|---|
| author | Silber, Zdeněk |
| author_facet | Silber, Zdeněk |
| contents | We investigate possible quantifications of Banach-Saks sets and weak Banach-Saks sets of higher orders and their relations to other quantities. We prove a quantitative version of the characterization of weak $ξ$-Banach-Saks sets using $\ell_1^{ξ+1}$-spreading models and a quantitative version of the relation of $ξ$-Banach-Saks sets, weak $ξ$-Banach-Saks sets, norm compactness and weak compactness. We further introduce a new measure of weak compactness. Finally, we provide some examples showing the limitations of these quantifications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_12773 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Quantification of Banach-Saks properties of higher orders Silber, Zdeněk Functional Analysis 46B20, 46B50 We investigate possible quantifications of Banach-Saks sets and weak Banach-Saks sets of higher orders and their relations to other quantities. We prove a quantitative version of the characterization of weak $ξ$-Banach-Saks sets using $\ell_1^{ξ+1}$-spreading models and a quantitative version of the relation of $ξ$-Banach-Saks sets, weak $ξ$-Banach-Saks sets, norm compactness and weak compactness. We further introduce a new measure of weak compactness. Finally, we provide some examples showing the limitations of these quantifications. |
| title | Quantification of Banach-Saks properties of higher orders |
| topic | Functional Analysis 46B20, 46B50 |
| url | https://arxiv.org/abs/2111.12773 |