The Dieudonné property on 𝐶(𝐾,𝐸)

Bombal, Fernando; Cembranos, Pilar

doi:10.1090/S0002-9947-1984-0752496-9

The Dieudonné property on $C(K, E)$
HTML articles powered by AMS MathViewer

by Fernando Bombal and Pilar Cembranos PDF

Trans. Amer. Math. Soc. 285 (1984), 649-656 Request permission

Abstract:

In this paper we prove that if $E$ is a Banach space with separable dual, then the space $C(K,E)$ of all continuous $E$-valued functions on a compact Hausdorff topological space $K$ has the Dieudonné property.

References

Jürgen Batt and E. Jeffrey Berg, Linear bounded transformations on the space of continuous functions. , J. Functional Analysis 4 (1969), 215–239. MR 0248546, DOI 10.1016/0022-1236(69)90012-3
W. J. Davis, T. Figiel, W. B. Johnson, and A. Pełczyński, Factoring weakly compact operators, J. Functional Analysis 17 (1974), 311–327. MR 0355536, DOI 10.1016/0022-1236(74)90044-5
J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964, DOI 10.1090/surv/015
Ivan Dobrakov, On representation of linear operators on $C_{0}\,(T,\,{\rm {\bf }X})$, Czechoslovak Math. J. 21(96) (1971), 13–30. MR 276804, DOI 10.21136/CMJ.1971.101000
A. Grothendieck, Sur les applications linéaires faiblement compactes d’espaces du type $C(K)$, Canad. J. Math. 5 (1953), 129–173 (French). MR 58866, DOI 10.4153/cjm-1953-017-4
Richard B. Holmes, Geometric functional analysis and its applications, Graduate Texts in Mathematics, No. 24, Springer-Verlag, New York-Heidelberg, 1975. MR 0410335, DOI 10.1007/978-1-4684-9369-6
Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. I, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 92, Springer-Verlag, Berlin-New York, 1977. Sequence spaces. MR 0500056, DOI 10.1007/978-3-642-66557-8

Banach spaces of continuous functions