The free Banach lattices generated by ℓp and c0
We prove that, when 2<p<∞, in the free Banach lattice generated by ℓp (respectively by c0), the absolute values of the canonical basis form an ℓr-sequence, where 1r=12+1p (respectively an ℓ2-sequence). In particular, in any Banach lattice, the absolute values of any ℓp sequence always have an...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositorio: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/204178 |
| Acceso en línea: | http://hdl.handle.net/10261/204178 |
| Access Level: | acceso abierto |
| Palabra clave: | Banach lattice Free lattice Weakly compactly generated space |
| Sumario: | We prove that, when 2<p<∞, in the free Banach lattice generated by ℓp (respectively by c0), the absolute values of the canonical basis form an ℓr-sequence, where 1r=12+1p (respectively an ℓ2-sequence). In particular, in any Banach lattice, the absolute values of any ℓp sequence always have an upper ℓr-estimate. Quite surprisingly, this implies that the free Banach lattices generated by the nonseparable ℓp(Γ) for 2<p<∞, as well as c0(Γ), are weakly compactly generated whereas this is not the case for 1≤p≤2. |
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