A Banach space with $L$-orthogonal sequences but without $L$-orthogonal elements
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910780755017728 |
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| author | Avilés, Antonio Martínez-Cervantes, Gonzalo Poveda, Alejandro Sáenz, Luís |
| author_facet | Avilés, Antonio Martínez-Cervantes, Gonzalo Poveda, Alejandro Sáenz, Luís |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06537 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Banach space with $L$-orthogonal sequences but without $L$-orthogonal elements Avilés, Antonio Martínez-Cervantes, Gonzalo Poveda, Alejandro Sáenz, Luís Logic Functional Analysis 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. |
| title | A Banach space with $L$-orthogonal sequences but without $L$-orthogonal elements |
| topic | Logic Functional Analysis |
| url | https://arxiv.org/abs/2501.06537 |