A double-dual characterization of separable Banach spaces containing \(\ell^1\). (English) Zbl 0312.46031


46B10 Duality and reflexivity in normed linear and Banach spaces
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[1] R. Baire,Sur les Fonctions des Variables Réelles, 1899, pp. 16, 30.
[2] S. Banach,Théorie des Operations Linéaires, Monografje Matematyczne, Warsaw, 1932.
[3] W. J. Davis, T. Figiel, W. B. Johnson and A. Pexczyński,Factoring weakly compact operators, J. Functional Analysis,17 (1974), 311–327. · Zbl 0306.46020
[4] L. E. Dor,On sequences spanning a complex l 1 space,47 (1975), 515–516. · Zbl 0296.46014
[5] F. Hausdorff,Set Theory, Chelsea Publ. Co., New York, 1962.
[6] R. C. James,A separable somewhat reflexive Banach space with nonseparable dual, Bull. Amer. Math. Soc.,80 (1974), 738–743. · Zbl 0286.46018
[7] J. L. Kelley and I. Namioka,Linear Topological Spaces, D. Van Nostrand Co., Princeton, New Jersey, 1963, p. 118. · Zbl 0115.09902
[8] R. D. McWilliams,A note on weak sequential convergence, Pacific J. Math.12 (1962), 333–335. · Zbl 0105.30801
[9] R. D. McWilliams,Iterated w*-sequential closure of a Banach space in its second conjugate, Proc. Amer. Math. Soc.14 (1963), 191–196. · Zbl 0113.09304
[10] R. D. McWilliams,On iterated w*-sequential closure of cones, Pacific J. Math.38 (1971), 697–715. · Zbl 0224.46011
[11] H. P. Rosenthal,A characterization of Banach spaces containing l 1, Proc. Nat. Acad. Sci. U.S.A.,71 (1974), 2411–2413. · Zbl 0297.46013
[12] H. P. Rosenthal,Pointwise compact subsets of the first Baire class, to appear. · Zbl 0392.54009
[13] G. Choquet,Remarques à propos de la démonstration de l’unicité de P. A. Meyer, Séminaire Brelot-Choquet-Deny (Théorie de Potential),6 (1962), No. 8, 13 pp. · Zbl 0115.32402
[14] R. Phelps,Lectures on Choquet’s Theorem, D. van Nostrand Co., Princeton, New Jersey, 1966. · Zbl 0135.36203
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