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Ultrabornological Bochner integrable function spaces

Published online by Cambridge University Press:  17 April 2009

J.C. Ferrando
J.C. Ferrando
Affiliation:
E.U. Informática Depto. Matematica Aplicada, Universidad Politécnica de Valencia Apartado, 22012, E-46071 Valencia, Spain
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Abstract

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If (Ω, Σ, μ) is a finite measure space and X is a normed space such that X* has the Radon-Nikodym property with respect to μ, we show first that each space Lp(μ, x), 1 < p < ∞, is ultrabornological whenever μ is atomless. When μ is arbitrary, we prove later on that the space Lp(μ, X) is ultrabornological if X* has the Radon-Nikodym property with respect to μ and X is itself an ultrabornological space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 47 , Issue 1 , February 1993 , pp. 119 - 126
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Beauzamy, B., Introduction to Banach spaces and their geometry, Mathematics Studies 68 (North Holland, 1982).Google Scholar
[2]Díaz, J.C., Florencio, M. and Paúl, P.J., ‘A uniform boundedness theorem for L∞(μ, E)’, Arch. Math, (to appear).Google Scholar
[3]Diestel, J., Sequences and series in Banach spaces, Graduate Texts in Math. 92 (Springer-Verlag, Berlin, Heidelberg, New York, 1984).CrossRefGoogle Scholar
[4]Diestel, J. and Uhl, J.J. Jr., Vector Measures, Mathematical Surveys No. 15. (A.M.S., Providence, Rhode Island, 1977).CrossRefGoogle Scholar
[5]Drewnowski, L., Florencio, M. and Paúl, P.J., ‘The space of Pettis integrable functions is barrelled’, Proc. Amer. Math. Soc. 114 (1992), 687–694.CrossRefGoogle Scholar
[6]Carreras, P. Pérez and Bonet, J., Barrelled locally convex spaces, Mathematics Studies 131 (North Holland, 1987).Google Scholar