The Fréchet space ces(p+), 1 <
[EN] The Banach spaces ces(p), 1 < p < infinity, were intensively studied by G. Bennett and others. The largest solid Banach lattice in C-N which contains l(p) and which the Cesaro operator C : C-N -> C-N maps into l(P) is ces(p). For each 1 <= p < infinity, the (p...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/107410 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/107410 |
| Access Level: | acceso abierto |
| Palabra clave: | Fréchet spaces sequence spaces power series spaces Schwartz spaces Fréchet lattices MATEMATICA APLICADA |
| Sumario: | [EN] The Banach spaces ces(p), 1 < p < infinity, were intensively studied by G. Bennett and others. The largest solid Banach lattice in C-N which contains l(p) and which the Cesaro operator C : C-N -> C-N maps into l(P) is ces(p). For each 1 <= p < infinity, the (positive) operator C also maps the Frechet space l(p+) = boolean AND(q > p) l(q) into itself. It is shown that the largest solid Frechet lattice in C-N which contains l(p+) and which C maps into l(p+) is precisely ces(p+) := boolean AND(q > p) ces(q). Although the spaces l(p+) are well understood, it seems that the spaces ces(p+) have not been considered at all. A detailed study of the Frechet spaces ces(p+),1 <= p < infinity, is undertaken. They are very different to the Frechet spaces l(p+) which generate them in the above sense. We prove that each ces(p+) is a power series space of finite type and order one, and that all the spaces ces(p+), 1 <= p < infinity, are isomorphic. (C) 2017 Elsevier Inc. All rights reserved. |
|---|