Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A stability property of a class of Banach spaces not containing a complemented copy of $ l\sb{1}$

Authors: Elias Saab and Paulette Saab
Journal: Proc. Amer. Math. Soc. 84 (1982), 44-46
MSC: Primary 46B20; Secondary 46E15
MathSciNet review: 633274
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ E$ be a Banach space and $ K$ be a compact Hausdorff space. The space $ C(K,E)$ will stand for the Banach space of all continuous $ E$-valued functions on $ K$ equipped with the sup norm. It is shown that the space $ E$ does not contain a complemented subspace isomorphic to $ {l_1}$ if and only if $ C(K,E)$ has the same property.

References [Enhancements On Off] (What's this?)

  • [1] C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 17 (1958), 151–164. MR 0115069
  • [2] J. Bourgain, An averaging result for 𝑐₀-sequences, Bull. Soc. Math. Belg. 30 (1978), no. 1, 83–87. MR 549653
  • [3] J. Diestel and J. J. Uhl Jr., Vector measures, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis; Mathematical Surveys, No. 15. MR 0453964
  • [4] N. Dinculeanu, Vector measures, Hochschulbücher für Mathematik, Band 64, VEB Deutscher Verlag der Wissenschaften, Berlin, 1966. MR 0206189
    N. Dinculeanu, Vector measures, International Series of Monographs in Pure and Applied Mathematics, Vol. 95, Pergamon Press, Oxford-New York-Toronto, Ont.; VEB Deutscher Verlag der Wissenschaften, Berlin, 1967. MR 0206190
  • [5] S. Kwapien, Sur les espaces de Banach contenant $ {c_0}$, Studia Math. 52 (1974), 187-188.
  • [6] Gilles Pisier, Une propriété de stabilité de la classe des espaces ne contenant pas 𝑙¹, C. R. Acad. Sci. Paris Sér. A-B 286 (1978), no. 17, A747–A749 (French, with English summary). MR 0511805
  • [7] Paulette Saab, The Choquet integral representation in the affine vector-valued case, Aequationes Math. 20 (1980), no. 2-3, 252–262. MR 577491,

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46B20, 46E15

Retrieve articles in all journals with MSC: 46B20, 46E15

Additional Information

Keywords: Complemented subspaces, vector measures
Article copyright: © Copyright 1982 American Mathematical Society