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Abstract Cesàro spaces: integral representations

Opened Access Abstract Cesàro spaces: integral representations

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Autor: Curbera Costello, Guillermo
Ricker, Werner J.
Departamento: Universidad de Sevilla. Departamento de Análisis Matemático
Fecha: 2016-09-01
Publicado en: Journal of Mathematical Analysis and Applications, 441 (1), 25-44.
Tipo de documento: Artículo
Resumen: The Cesàro function spaces Cesp = [C, Lp ], 1 ≤ p ≤ ∞, have received renewed attention in recent years. Many properties of [C, Lp ] are known. Less is known about [C, X] when the Ces`aro operator takes its values in a rearrangement invariant (r.i.) space X other than Lp . In this paper we study the spaces [C, X] via the methods of vector measures and vector integration. These techniques allow us to identify the absolutely continuous part of [C, X] and the Fatou completion of [C, X]; to show that [C, X] is never reflexive and never r.i.; to identify when [C, X] is weakly sequentially complete, when it is isomorphic to an AL-space, and when it has the Dunford-Pettis property. The same techniques are used to analyze the operator C : [C, X] → X; it is never compact but, it can be completely continuous.
Cita: Curbera Costello, G. y Ricker, W.J. (2016). Abstract Cesàro spaces: integral representations. Journal of Mathematical Analysis and Applications, 441 (1), 25-44.
Tamaño: 284.1Kb
Formato: PDF

URI: http://hdl.handle.net/11441/42870

DOI: http://dx.doi.org/10.1016/j.jmaa.2016.03.074

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