Identificador persistente para citar o vincular este elemento: http://hdl.handle.net/10662/14511
Títulos: Type II-ʌ-Weak Radon-Nikodym property in a Banach space associated with a compact metrizable Abelian group
Autores/as: Chakraborty, N. D.
Jaker Ali, Sk.
Palabras clave: Grupo abeliano compacto metrizable;Funciones integrables Pettis;Conjuntos Riesz;Tipo II-ʌ-propiedad débil de Radon-Nikodym;Compact metrizable abelian group;Pettis integrable functions;Riesz sets;Type II-ʌ-weak Radon-Nikodym property
Fecha de publicación: 2008
Editor/a: Universidad de Extremadura, Servicio de Publicaciones
Resumen: Let G be a compact metrizable abelian group with normalized Haar measure λ, Ґ the dual group of G and ʌ a subset of Ґ. Let X be a Banach space and f : G → X be a Pettis integrable function with respect to Ґ. It has been shown that the set {𝑓(𝛶):𝛶𝜀 ʌ} of the Fourier coefficients of 𝑓 is a relatively norm compact subset of X. We have shown by a counter-example that the converse of this result is not true, in general. We have introduced the idea of type II-ʌ-Weak Radon-Nikodym property (type II-ʌ-WRNP) of X and have shown that the converse is true for X having this property when ʌ is a Riesz set. We have also obtained several necessary and sufficient conditions for X to possess this property when ʌ is a Riesz set.
URI: http://hdl.handle.net/10662/14511
ISSN: 0213-8743
Colección:Extracta Mathematicae Vol. 23, nº 3 (2008)

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