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  • Cited by 4
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Leung, Denny H. 1993. Banach spaces with property (w). Glasgow Mathematical Journal, Vol. 35, Issue. 02, p. 207.

    Emmanuele, G. 1991. On the reciprocal Dunford-Pettis property in projective tensor products. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 109, Issue. 01, p. 161.

    Bombal, Fernando Cembranos, Pilar and Mendoza, José 1990. On the surjective Dunford-Pettis Property. Mathematische Zeitschrift, Vol. 204, Issue. 1, p. 373.

    Bombal, Fernando and Cembranos, Pilar 1985. Characterization of some classes of operators on spaces of vector-valued continuous functions. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 97, Issue. 01, p. 137.

  • Bulletin of the Australian Mathematical Society, Volume 28, Issue 2
  • October 1983, pp. 175-186

On Banach spaces of vector valued continuous functions

  • Pilar Cembranos (a1)
  • DOI:
  • Published online: 01 October 1983

Let K be a compact Hausdorff space and let E be a Banach space. We denote by C(K, E) the Banach space of all E-valued continuous functions defined on K, endowed with the supremum norm.

Recently, Talagrand [Israel J. Math.44 (1983), 317–321] constructed a Banach space E having the Dunford-Pettis property such that C([0, 1], E) fails to have the Dunford-Pettis property. So he answered negatively a question which was posed some years ago.

We prove in this paper that for a large class of compacts K (the scattered compacts), C(K, E) has either the Dunford-Pettis property, or the reciprocal Dunford-Pettis property, or the Dieudonné property, or property V if and only if E has the same property.

Also some properties of the operators defined on C(K, E) are studied.

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[1]Jürgen Batt and E. Jeffrey Berg , “Linear bounded transformations on the space of continuous functions”, J. Funct. Anal. 4 (1969), 215239.

[2]J. Diestel and J.J. Uhl Jr, Vector measures (Mathematical Surveys, 15. American Mathematical Society, Providence, Rhode Island, 1977).

[4]A. Grothendieck , “Sur les applications lineaires faiblement compactes d'espaces du type C(K)”, Canad. J. Math. 5 (1953), 129173.

[6]Joram Lindenstrauss , Lior Tzafriri , Classical Banach spaces. I. Sequence spaces (Ergebnisse der Mathematik und ihrer Grenzgebiete, 92. Springer-Verlag, Berlin, Heidelberg, New York, 1977).

[9]M. Talagrand , “La propriété de Dunford-Pettis dans C(K, E) et L1(E)”, Israel J. Math. 44 (1983), 317321.

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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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