Maximal inequalities, frames and greedy algorithms
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918270883332096 |
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| author | Berná, Pablo Freeman, Daniel Oikhberg, Timur Taylor, Mitchell |
| author_facet | Berná, Pablo Freeman, Daniel Oikhberg, Timur Taylor, Mitchell |
| contents | The aim of this article is to use Banach lattice techniques to study coordinate systems in function spaces. We begin by proving that the greedy algorithm of a basis is order convergent if and only if a certain maximal inequality is satisfied. We then show that absolute frames need not admit a reconstruction algorithm with respect to the usual order convergence, but do allow for reconstruction with respect to the order convergence inherited from the double dual. After this, we investigate the extent to which such coordinate systems affect the geometry of the underlying function space. Most notably, we prove that a Banach lattice $X$ is lattice isomorphic to a closed sublattice of a $C(K)$-space if and only if every unconditional sequence in $X$ is absolute. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01047 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximal inequalities, frames and greedy algorithms Berná, Pablo Freeman, Daniel Oikhberg, Timur Taylor, Mitchell Functional Analysis 46B42, 46B15, 41A65 The aim of this article is to use Banach lattice techniques to study coordinate systems in function spaces. We begin by proving that the greedy algorithm of a basis is order convergent if and only if a certain maximal inequality is satisfied. We then show that absolute frames need not admit a reconstruction algorithm with respect to the usual order convergence, but do allow for reconstruction with respect to the order convergence inherited from the double dual. After this, we investigate the extent to which such coordinate systems affect the geometry of the underlying function space. Most notably, we prove that a Banach lattice $X$ is lattice isomorphic to a closed sublattice of a $C(K)$-space if and only if every unconditional sequence in $X$ is absolute. |
| title | Maximal inequalities, frames and greedy algorithms |
| topic | Functional Analysis 46B42, 46B15, 41A65 |
| url | https://arxiv.org/abs/2601.01047 |