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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