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Duals of vector-valued Köthe function spaces

Published online by Cambridge University Press:  24 October 2008

Miguel Florencio ,
Pedro J. Paúl  and
Carmen Sáez
Miguel Florencio
Affiliation:
E.S. Ingenieros Industriales, Avda, Reina Mercedes s/n, 41012 Sevilla, Spain
Pedro J. Paúl
Affiliation:
E.S. Ingenieros Industriales, Avda, Reina Mercedes s/n, 41012 Sevilla, Spain
Carmen Sáez
Affiliation:
E.S. Ingenieros Industriales, Avda, Reina Mercedes s/n, 41012 Sevilla, Spain
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Abstract

Let Λ be a perfect Köthe function space in the sense of Dieudonné, and Λ× its Köthe-dual. Let E be a normed space. Then the topological dual of the space Λ(E) of Λ-Bochner integrable functions equals the corresponding Λ×(E′) if and only if E′ has the Radon–Nikodým property. We also give some results concerning barrelledness for spaces of this kind.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 1 , July 1992 , pp. 165 - 174
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

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