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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

REFERENCES

[1]Clauzuee, P.. Contribution a l'étude topologique et geometrique d'espaces de type Köthe-Orlicz. These, Université des Ciencies et Techniques du Languedoc, Montpellier (1985).Google Scholar
[2]Diestel, J. and Uhl, J. J. Jr. Vector Measures. Mathematical Surveys and Monographs no. 15 (American Mathematical Society, 1977).Google Scholar
[3]Dieudonné, J.. Sur les espaces de Köthe. J. Analyse Math. 1 (1951), 81–115.CrossRefGoogle Scholar
[4]Florencio, M., Paúl, P. J. and Sáez, C.. A note on the Köthe dual of Banach-valued echelon spaces. Collect. Math. 39 (1988), 257–261.Google Scholar
[5]Drewnowki, L., Florencio, M. and Paúl, P. J.. Barrelled function spaces. In Progress in Functional Analysis. Proceedings of the Peñíscola Meeting 1990, on the occasion of the 60th birthday of Professor M. Valdivia (editors Bierstedt, K. D. et al. ), Mathematical Studies no. 170 (North-Holland, 1992), pp. 191–199.Google Scholar
[6]Lluch, C. Jordán and Sánchez, J. R. Torregrosa. A characterization of the duals of some echelon Köthe spaces. Collect. Math. 38 (1987), 229–248.Google Scholar
[7]Köthe, G.. Topological Vector Spaces, vol. 1 (Springer-Verlag, 1969).Google Scholar
[8]Macdonald, A. L.. Vector valued Köthe function spaces. I. Illinois J. Math. 17 (1973), 533–545. II. Illinois J. Math. 17 (1973), 546–557. III. Illinois J. Math. 18 (1974), 136–146.Google Scholar
[9]Phuong-Các, N.. Generalized Köthe function spaces. I. Proc. Cambridge Philos. Soc. 65 (1969), 601–611.CrossRefGoogle Scholar
[10]Rosier, R. C.. Dual spaces of certain vector sequence spaces. Pacific J. Math. 46 (1973), 487–501.CrossRefGoogle Scholar