A Banach space with $L$-orthogonal sequences but without $L$-orthogonal elements
Logic
2025-01-14 v1 Functional Analysis
Abstract
We prove that the existence of Banach spaces with -orthogonal sequences but without -orthogonal elements is independent of the standard foundation of Mathematics, ZFC. This provides a definitive answer to \cite[Question~1.1]{AvilesMartinezRueda}. Generalizing classical -point ultrafilters, we introduce the notion of -measures and provide several results generalizing former theorems by Miller \cite{Miller} and Bartoszynski \cite{Bartoszynski} for -point ultrafilters.
Cite
@article{arxiv.2501.06537,
title = {A Banach space with $L$-orthogonal sequences but without $L$-orthogonal elements},
author = {Antonio Avilés and Gonzalo Martínez-Cervantes and Alejandro Poveda and Luís Sáenz},
journal= {arXiv preprint arXiv:2501.06537},
year = {2025}
}