Spectral properties of generalized Cesaro operators in sequence spaces

[EN] The generalized Cesaro operators C-t, for t is an element of[0, 1], were first investigated in the 1980s. They act continuously in many classical Banach sequence spaces contained in C(N)0, such as l(p), c(0), c, bv(0), bv and, as recently shown in Curbera et al. (J Math Anal Appl 507:31, 2022)...

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Detalhes bibliográficos
Autores: Albanese, Angela A., Ricker, Werner J., Bonet Solves, José Antonio|||0000-0002-9096-6380
Formato: artículo
Fecha de publicación:2023
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/204835
Acesso em linha:https://riunet.upv.es/handle/10251/204835
Access Level:acceso abierto
Palavra-chave:Generalized Cesaro operator
Compactness
Spectra
Power boundedness
Uniform mean ergodicity
Sequence space
Frechet space
(LB)-space
MATEMATICA APLICADA
Descrição
Resumo:[EN] The generalized Cesaro operators C-t, for t is an element of[0, 1], were first investigated in the 1980s. They act continuously in many classical Banach sequence spaces contained in C(N)0, such as l(p), c(0), c, bv(0), bv and, as recently shown in Curbera et al. (J Math Anal Appl 507:31, 2022) [26], also in the discrete Cesaro spaces ces(p) and their (isomorphic) dual spaces d(p). In most cases C-t (t not equal 1) is compact and its spectra and point spectrum, together with the corresponding eigenspaces, are known. We study these properties of C-t, as well as their linear dynamics and mean ergodicity, when they act in certain non-normable sequence spaces contained in C(N)0. Besides C(N)0 itself, the Frechet spaces considered are l(p+), ces(p+) and d( p+), for 1 <= p < infinity, as well as the (LB)-spaces l(p-), ces(p-) and d(p-), for 1 < p <= infinity.