Quasi-greedy bases in ℓp (0 < p < 1) are democratic
The list of known Banach spaces whose linear geometry determines the (nonlinear) democracy functions of their quasi-greedy bases to the extent that they end up being democratic, reduces to c0, ℓ2, and all separable L1-spaces. Oddly enough, these are the only Banach spaces that, when they have an unc...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad Pública de Navarra |
| Repositorio: | Academica-e. Repositorio Institucional de la Universidad Pública de Navarra |
| OAI Identifier: | oai:academica-e.unavarra.es:2454/40416 |
| Acceso en línea: | https://hdl.handle.net/2454/40416 |
| Access Level: | acceso abierto |
| Palabra clave: | Democratic basis Quasi-Banach spaces Quasi-greedy basis Sequence spaces |
| Sumario: | The list of known Banach spaces whose linear geometry determines the (nonlinear) democracy functions of their quasi-greedy bases to the extent that they end up being democratic, reduces to c0, ℓ2, and all separable L1-spaces. Oddly enough, these are the only Banach spaces that, when they have an unconditional basis, it is unique. Our aim in this paper is to study the connection between quasi-greediness and democracy of bases in non-locally convex spaces. We prove that all quasi-greedy bases in ℓp for 0<p<1 (which also has a unique unconditional basis) are democratic with fundamental function of the same order as (m1/p)∞m=1. The methods we develop allow us to obtain even more, namely that the same occurs in any separable Lp-space, 0<p<1, with the bounded approximation property. |
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