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The bidual of the space of polynomials on a Banach space

Published online by Cambridge University Press:  01 November 1997

J. A. JARAMILLO ,
A. PRIETO  and
I. ZALDUENDO
J. A. JARAMILLO
Affiliation:
Departamento de Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid, España
A. PRIETO
Affiliation:
Departamento de Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid, España
I. ZALDUENDO
Affiliation:
Departamento de Economía y Matemática, Universidad de San Andrés, CC 1983 Correo Central, (1000) Buenos Aires, Argentina
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Abstract

Questions concerning extensions of polynomials or analytic functions from a Banach space E to its bidual E", and others about reflexivity and related properties on spaces of homogeneous polynomials Pk(E), have recently spurred interest regarding the structure of the bidual of a space of polynomials [4, 14, 22].

In this paper we study the relationship between the bidual of Pk(E) and the space of polynomials over E". We define a map through which elements of the bidual of Pk(E) may be viewed as polynomials over E"

formula here

and study this map to obtain information about Pk(E)". We have tried as far as possible to avoid imposing restricting conditions on E.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 122 , Issue 3 , November 1997 , pp. 457 - 471
Copyright
Cambridge Philosophical Society 1997

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