The Hereditary Dunford-Pettis Property On C(K,E)

The author studies the hereditary Dunford-Pettis property for spaces CX(K) of continuous Xvalued functions (X a Banach space) on a compact Hausdorff space K. First, she shows that CX(K) has the hereditary Dunford-Pettis property if and only if one of the following holds: (a) K is finite andX has the...

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Detalles Bibliográficos
Autor: Cembranos Díaz, María Del Pilar
Tipo de recurso: artículo
Fecha de publicación:1987
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/64613
Acceso en línea:https://hdl.handle.net/20.500.14352/64613
Access Level:acceso abierto
Palabra clave:517
Mathematics
Análisis matemático
Análisis funcional y teoría de operadores
1202 Análisis y Análisis Funcional
Descripción
Sumario:The author studies the hereditary Dunford-Pettis property for spaces CX(K) of continuous Xvalued functions (X a Banach space) on a compact Hausdorff space K. First, she shows that CX(K) has the hereditary Dunford-Pettis property if and only if one of the following holds: (a) K is finite andX has the hereditary Dunford-Pettis property; (b) C(K) and c0(X) have the hereditary Dunford-Pettis property. Unwilling to give up here, the author provides an elegant characterization of when c0(X) has the hereditary Dunford-Pettis property. Since the paper was written, Nunez has provided an elegant example (based on work of Talagrand) of an X such that, while X is hereditarily Dunford-Pettis, c0(X) is not. Remarkable and satisfying!