On Unconditionality and Higher-Order Schreier Unconditionality

2025/10/03 by Shiliaev, Mark
#41A65 #46B15 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2510.02783

Abstract

Let X be a Banach space, (e_n)_n=1^∞ 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.

Citations

• Characterizations of almost greedy and partially greedy bases
• Unconditional structures of weakly null sequences
• Convex unconditionality and summability of weakly null sequences
• Complexity of weakly null sequences
• On Schreier unconditional sequences

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