Zoo of ideal Schauder basis
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915470068678656 |
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| author | Kwela, Adam Swaczyna, Jarosław |
| author_facet | Kwela, Adam Swaczyna, Jarosław |
| contents | We investigate the notion of filter (equivalently: ideal) Schauder basis of a Banach space. We do so by providing bunch of new examples of such bases that are not the standard ones, especially within classical Banach spaces ($\ell_p$, $c_0$, James' space). Those examples lead to distinguishing and characterizing filters (equivalently: ideals) in terms of Schauder bases. We investigate the relationship between possibly basic sequences and filters (equivalently: ideals) on the set of natural numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21235 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Zoo of ideal Schauder basis Kwela, Adam Swaczyna, Jarosław Functional Analysis Logic 46B15, 03E15, 03E75 (Primary) 46B20, 54A20 (Secondary) We investigate the notion of filter (equivalently: ideal) Schauder basis of a Banach space. We do so by providing bunch of new examples of such bases that are not the standard ones, especially within classical Banach spaces ($\ell_p$, $c_0$, James' space). Those examples lead to distinguishing and characterizing filters (equivalently: ideals) in terms of Schauder bases. We investigate the relationship between possibly basic sequences and filters (equivalently: ideals) on the set of natural numbers. |
| title | Zoo of ideal Schauder basis |
| topic | Functional Analysis Logic 46B15, 03E15, 03E75 (Primary) 46B20, 54A20 (Secondary) |
| url | https://arxiv.org/abs/2508.21235 |