On Unconditionality and Higher-Order Schreier Unconditionality
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915531821416448 |
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| author | Shiliaev, Mark |
| author_facet | Shiliaev, Mark |
| contents | Let $X$ be a Banach space, $(e_n)_{n=1}^\infty$ be its basis, and $S_α$ be a Schreier family of order alpha. We introduce Condition A which is a weaker version of the Continuum Hypothesis. Granted Condition A, we show that if the basis $(e_n)$ is $S_α$-unconditional for every countable ordinal alpha, then it is unconditional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02783 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Unconditionality and Higher-Order Schreier Unconditionality Shiliaev, Mark Functional Analysis 41A65, 46B15 Let $X$ be a Banach space, $(e_n)_{n=1}^\infty$ be its basis, and $S_α$ be a Schreier family of order alpha. We introduce Condition A which is a weaker version of the Continuum Hypothesis. Granted Condition A, we show that if the basis $(e_n)$ is $S_α$-unconditional for every countable ordinal alpha, then it is unconditional. |
| title | On Unconditionality and Higher-Order Schreier Unconditionality |
| topic | Functional Analysis 41A65, 46B15 |
| url | https://arxiv.org/abs/2510.02783 |