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...

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Detalles Bibliográficos
Autores: Bonet Solves, José Antonio|||0000-0002-9096-6380, Ricker, Werner J.
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
Descripción
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.