Opened Access Extended eigenvalues for Cesàro operators

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Autor: Lacruz Martín, Miguel Benito
León Saavedra, Fernando
Petrovic, Srdjan
Zabeti, Omid
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2015-09-15
Publicado en: Journal of Mathematical Analysis and Applications, 429 (2), 623-657.
Tipo de documento: Artículo
Resumen: A complex scalar λ is said to be an extended eigenvalue of a bounded linear operator T on a complex Banach space if there is a nonzero operator X such that T X = λXT. Such an operator X is called an extended eigenoperator of T corresponding to the extended eigenvalue λ. The purpose of this paper is to give a description of the extended eigenvalues for the discrete Ces`aro operator C0, the finite continuous Ces`aro operator C1 and the infinite continuous Ces`aro operator C∞ defined on the complex Banach spaces ℓ p , Lp [0, 1] and L p [0, ∞) for 1 < p < ∞ by the expressions (C0f)(n): = 1 n + 1 Xn k=0 f(k), (C1f)(x): = 1 x Z x 0 f(t) dt, (C∞f)(x): = 1 x Z x 0 f(t) dt. It is shown that the set of extended eigenvalues for C0 is the interval [1, ∞), for C1 it is the interval (0, 1], and for C∞ it reduces to the singleton {1}.
Cita: Lacruz Martín, M.B., León Saavedra, F., Petrovic, S. y Zabeti, O. (2015). Extended eigenvalues for Cesàro operators. Journal of Mathematical Analysis and Applications, 429 (2), 623-657.
Tamaño: 353.5Kb
Formato: PDF

URI: http://hdl.handle.net/11441/43531

DOI: 10.1016/j.jmaa.2015.04.028

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