Enlarge Greedy Sums in Greedy-Type Properties by Different Factors
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911311297773568 |
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| author | Chu, Hung Viet |
| author_facet | Chu, Hung Viet |
| contents | It was previously known that the almost greedy (AG) property essentially remains the same when we enlarge greedy sums in the classical definition by a factor $λ\geqslant 1$. The present paper shows that if instead, we enlarge greedy sums in a reformulation of the AG property, we obtain a weaker one. However, the new property is essentially independent of the enlarging factor $λ$ once $λ> 1$. In contrast, we observe a continuum of partially greedy-like properties by varying $λ\in [1,\infty)$. Last but not least, under a threshold for $λ$, we characterize the isometric version of the weakened AG property. Specifically, the characterization holds if and only if $λ\in [1, 2]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09604 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enlarge Greedy Sums in Greedy-Type Properties by Different Factors Chu, Hung Viet Functional Analysis 41A65, 46B15 It was previously known that the almost greedy (AG) property essentially remains the same when we enlarge greedy sums in the classical definition by a factor $λ\geqslant 1$. The present paper shows that if instead, we enlarge greedy sums in a reformulation of the AG property, we obtain a weaker one. However, the new property is essentially independent of the enlarging factor $λ$ once $λ> 1$. In contrast, we observe a continuum of partially greedy-like properties by varying $λ\in [1,\infty)$. Last but not least, under a threshold for $λ$, we characterize the isometric version of the weakened AG property. Specifically, the characterization holds if and only if $λ\in [1, 2]$. |
| title | Enlarge Greedy Sums in Greedy-Type Properties by Different Factors |
| topic | Functional Analysis 41A65, 46B15 |
| url | https://arxiv.org/abs/2512.09604 |