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arXiv · 2510.02783

On Unconditionality and Higher-Order Schreier Unconditionality

Mark Shiliaev
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Abstract

Let $X$ be a Banach space, $(e_n)_{n=1}^\infty$ be its basis, and $S_\alpha$ 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 $S_\alpha$-unconditional for every countable ordinal alpha, then it is unconditional.

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Mark Shiliaev. 2025-10-03. On Unconditionality and Higher-Order Schreier Unconditionality. https://arxiv.org/abs/2510.02783

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