Order spectrum of the Cesàro operator in Banach lattice sequence spaces
[EN] The discrete Cesàro operator C acts continuously in various classical Banach sequence spaces within CN. For the coordinatewise order, many such sequence spaces X are also complex Banach lattices [eg. c0,¿p for 1<p¿¿, and ces(p) for p¿{0}¿(1,¿)]. In such Banach lattice sequence spaces, C...
| 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:10251/176110 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/176110 |
| Access Level: | acceso abierto |
| Palabra clave: | Banach algebra Banach sequence space Cesàro operator Spectrum Order spectrum MATEMATICA APLICADA |
| Sumario: | [EN] The discrete Cesàro operator C acts continuously in various classical Banach sequence spaces within CN. For the coordinatewise order, many such sequence spaces X are also complex Banach lattices [eg. c0,¿p for 1<p¿¿, and ces(p) for p¿{0}¿(1,¿)]. In such Banach lattice sequence spaces, C is always a positive operator. Hence, its order spectrum is well defined within the Banach algebra of all regular operators on X. The purpose of this note is to show, for every X belonging to the above list of Banach lattice sequence spaces, that the order spectrum ¿o(C) of Ccoincides with its usual spectrum ¿(C) when C is considered as a continuous linear operator on the Banach space X. |
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