Operators acting in the dual spaces of discrete Cesàro spaces
[EN] The discrete Cesaro (Banach) sequence spaces ces(r),1<r<infinity, have been thoroughly investigated for over 45 years. Not so for their dual spaces d(s) approximately equal to (ces(r))', which are somewhat unwieldy. Our aim is to undertake a further study of the spaces d(...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| 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:10251/161155 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/161155 |
| Access Level: | acceso abierto |
| Palabra clave: | Banach sequence space Cesaro operator Regular operator Multiplier MATEMATICA APLICADA |
| Sumario: | [EN] The discrete Cesaro (Banach) sequence spaces ces(r),1<r<infinity, have been thoroughly investigated for over 45 years. Not so for their dual spaces d(s) approximately equal to (ces(r))', which are somewhat unwieldy. Our aim is to undertake a further study of the spaces d(s) and of various operators acting between these spaces. It is shown that d(s)subset of d(t) whenever s <= t, with the inclusion being compact if s<t.The classical Cesaro operator C is continuous from d(s) into d(t) precisely when s <= t and compact precisely when s<t. Moreover, C even maps the larger space ces(s) continuously into d(s). This is a consequence of the Hardy-Littlewood maximal theorem and the remarkable property, for each 1<s<infinity, that x is an element of CN if and only if C(|x|)is an element of d(s). These results are used to analyze the spectrum and to determine the norm and the mean ergodicity of C acting in d(s). Similar properties for multiplier operators are also treated. |
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