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On the Dunford-Pettis property in spaces of vector-valued bounded functions

  • Manuel D. Contreras (a1) and Santiago Díaz (a1)
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We show that L∞(μ,X) has the Dunford-Pettis property for some classical Banach spaces including L1(μ), C (K), the disc algebra A and H∞.

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Copyright
COPYRIGHT: © Australian Mathematical Society 1996
References
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[1]Bombal, F., ‘On weakly compact operators on spaces of vector valued continuous functions’, Proc. Amer. Math. Soc. 97 (1986), 93–96.
[2]Bombal, F., ‘Distinguished subsets in vector sequence spaces’, in Progress in Functional Analysis, (Bierstedt, K.D., Bonet, J., Horváth, J. and Maestre, M., Editors) (North-Holland/Elsevier Science Publishers B.V., Amsterdam, New York, Oxford, 1992), pp. 293–306.
[3]Bourgain, J., ‘On the Dunford-Pettis property’, Proc. Amer. Math. Soc. 81 (1981), 265–272.
[4]Contreras, M.D. and Díaz, S., ‘C (K, A) and C (K, H ∞) have the Dunford-Pettis property’, Proc. Amer. Math. Soc. (to appear).
[5]Díaz, S., ‘Complemented copies of c 0 in L ∞(μ, X)’, Proc. Amer. Math. Soc. 120 (1994), 1167–1172.
[6]Diestel, J., ‘A survey of results related to the Dunford-Pettis property’, in Contemporary Math., 2, Proc. Of the Conf. on Integration, Topology and Geometry in Linear Spaces(Amer. Math. Soc.,Providence, RI,1980), pp. 15–60.
[7]Diestel, J. and Uhl, J.J. Jr, Vector measures, Math. Surveys, 15 (Amer. Math. Soc., Providence, RI, 1977).
[8]Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces, Lecture Notes in Mathematics, 338 (Springer-Verlag, Berlin, Heidelberg, New York, 1973).
[9]Talagrand, M., ‘La propriété de Dunford-Pettis dans C (K, E) et L 1(E)’, Israel J. Math. 44 (1983), 317–321.
[10]Wojtaszczyk, P., Banach Spaces for Analysts, Cambridge Studies in Advanced Mathematics, 25 (Cambridge University Press, Cambridge, 1991).
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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