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An ordered suprabarrelled space

Part of: Set functions and measures on spaces with additional structure

Published online by Cambridge University Press:  09 April 2009

J. C. Ferrando  and
M. López-Pellicer
M. López-Pellicer
Affiliation:
Departmento de Matemática Aplicada (ETSIA) Universidad Politécnica de ValenciaApartado 22012 46071-ValenciaSpain
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Abstract

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A locally convex space E is said to be ordered suprabarrelled if given any increasing sequence of subspaces of E covering E there is one of them which is suprabarrelled. In this paper we show that the space m0(X, Σ), where X is any set and Σ is a σ-algebra on X, is ordered suprabarrelled, given an affirmative answer to a previously raised question. We also include two applications of this result to the theory of vector measures.

Keywords

barrelled spacesuprabarrelled space.

MSC classification

Secondary: 28C99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 1 , August 1991 , pp. 106 - 117
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Diestel, J. and Faires, B., ‘On vector measures’, Trans. Amer. Math. Soc. 198 (1974), 253–271.CrossRefGoogle Scholar
[2]Diestel, J. and Uhl, J. R., Vector measures, Mathematical Surveys No. 15, Amer. Math. Soc., Providence, R.I., 1977.CrossRefGoogle Scholar
[3]Drewnowski, L., ‘An extension of a theorem of Rosenthal on operators acting from l ∞(Γ)’, Studia Math. 62 (1976), 209–215.CrossRefGoogle Scholar
[4]Ferrando, J. C. and López-Pellicer, M., ‘On ordered suprabarrelled spaces’, Arch. Math. 53 (1989), 405–410.Google Scholar
[5]Carreras, P. Pérez and Bonet, J., Barrelled locally convex spaces, North-Holland Math. Studies 131, Amsterdam, New York, Oxford, 1987.Google Scholar
[6]Rodríguez-Salinas, B., ‘Sobre la clase del espacio tonelado (Σ)’, Rev. Réal Acad. Ci. Madrid 74 Cuad. 50 (1980), 827–829.Google Scholar
[7]Saxon, S. A., ‘Nuclear and product spaces, Baire-like spaces and the strongest locally convex topology’, Math. Ann. 197 (1972), 87–106.CrossRefGoogle Scholar
[8]Valdivia, M., ‘On certain Barrelled normed spaces’, Ann. Inst. Fourier (Grenoble) 29 (1979), 39–56.CrossRefGoogle Scholar
[9]Valdivia, M., On suprabarrelled spaces, Funct. Anal. Holomorphy and Approximation Theory, Rio de Janeiro 1978, Lecture Notes in Math., Springer-Verlag, 1981, pp. 572–580.Google Scholar
[10]Valdivia, M., ‘Sobre el teorema de la gráfica cerrada’, Collect. Math. 22 (1971), 51–72.Google Scholar
[11]Ferrando, J. C. and López-Pefficer, M., ‘Strong barrelledness properties in (X, A) and bounded finite additive measures’, Math. Ann. 287 (1990), 727–736.CrossRefGoogle Scholar