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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
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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.


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  • [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, 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, 10.1007/BF02190517

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0633274-1
Keywords: Complemented subspaces, vector measures
Article copyright: © Copyright 1982 American Mathematical Society