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arXiv · 2501.06537

A Banach space with $L$-orthogonal sequences but without $L$-orthogonal elements

Antonio Avilés·Gonzalo Martínez-Cervantes·Alejandro Poveda·Luís Sáenz
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Abstract

We prove that the existence of Banach spaces with $L$-orthogonal sequences but without $L$-orthogonal elements is independent of the standard foundation of Mathematics, ZFC. This provides a definitive answer to \cite[Question~1.1]{AvilesMartinezRueda}. Generalizing classical $Q$-point ultrafilters, we introduce the notion of $Q$-measures and provide several results generalizing former theorems by Miller \cite{Miller} and Bartoszynski \cite{Bartoszynski} for $Q$-point ultrafilters.

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Antonio Avilés, Gonzalo Martínez-Cervantes, Alejandro Poveda, Luís Sáenz. 2025-01-11. A Banach space with $L$-orthogonal sequences but without $L$-orthogonal elements. https://arxiv.org/abs/2501.06537

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