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Rosenthal sets and the Radon-Nikodym property

  • Patrick N. Dowling (a1)
Abstract

Let X be a complex Banach space, G a compact abelian metrizable group and Λ a subset of Ĝ, the dual group of G. If X has the Radon-Nikodym property and is separable then has the Radon-Nikodym property. One consequence of this is that CΛ(G, X) has the Radon-Nikodym property whenever X has the Radon-Nikodym property and the Schur property and Λ is a Rosenthal set. A partial stability property for products of Rosenthal sets is also obtained.

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Copyright
COPYRIGHT: © Australian Mathematical Society 1993
References
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[1]Bukhvalov, A. V., ‘Radon-Nikodym property in Banach spaces of measurable vector- valued functions’, Mat. Zametki 26 (1979), 875–884.
English translation: Math. Notes 26 (1979), 939–944.
[2]Diestel, J. and Uhl, J. J. Jr, Vector Measures, Math. Surveys Monographs, 15 (Amer. Math. Soc., Providence, 1977).
[3]Diestel, J. and Uhl, J. J. Jr, ‘Progress in vector measures – 1977–1983’, in: Measure Theory and its Applications, Lecture Notes in Mathematics, 1033 (Springer, Berlin, 1983), pp. 144–192.
[4]Dunford, N. and Schwartz, J. T., Linear operators, Part 1 (Interscience Publishers, New York, 1957).
[5]Lust-Piquard, F., ‘Ensenbies de Rosenthal et ensembles de Riesz’, C. R. Acad. Sci. Paris Sér. I Math. 282 (1976), 833–835.
[6]Lust-Piquard, F., ‘L'espace des fonctions presque-periodiques dont le spectre est contenu dans un ensemble compact denombrable á la propriete de Schur’, Colloq. Math. 41 (1979), 273–284.
[7]Lust-Piquard, F., ‘Propriétés geometriques des sous-espaces invariants par translation de L1 (G) et C(G)’, Séminaire sur la geometrie des espaces de Banach, Ecole Polytechnique (1977–1978), Exposé 26.
[8]Lust-Piquard, F., ‘Propriétés harmoniques et geometriques des sous-espaces invariants par translation de L∞ (G)’, (Ph.D. Thesis, Université Paris-Sud, 1978).
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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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