×

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


MSC:

46B10 Duality and reflexivity in normed linear and Banach spaces
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] R. Baire,Sur les Fonctions des Variables Réelles, 1899, pp. 16, 30. · JFM 30.0359.01
[2] Banach, S., Théorie des Operations Linéaires (1932), Warsaw: Monografje Matematyczne, Warsaw · JFM 58.0420.01
[3] Davis, W. J.; Figiel, T.; Johnson, W. B.; Pexczyński, A., Factoring weakly compact operators, J. Functional Analysis, 17, 311-327 (1974) · Zbl 0306.46020 · doi:10.1016/0022-1236(74)90044-5
[4] Dor, L. E., On sequences spanning a complex l space, 47, 515-516 (1975) · Zbl 0296.46014
[5] Hausdorff, F., Set Theory (1962), New York: Chelsea Publ. Co., New York
[6] James, R. C., A separable somewhat reflexive Banach space with nonseparable dual, Bull. Amer. Math. Soc., 80, 738-743 (1974) · Zbl 0286.46018 · doi:10.1090/S0002-9904-1974-13580-9
[7] Kelley, J. L.; Namioka, I., Linear Topological Spaces, 118-118 (1963), Princeton, New Jersey: D. Van Nostrand Co., Princeton, New Jersey · Zbl 0115.09902
[8] McWilliams, R. D., A note on weak sequential convergence, Pacific J. Math., 12, 333-335 (1962) · Zbl 0105.30801
[9] McWilliams, R. D., Iterated w*-sequential closure of a Banach space in its second conjugate, Proc. Amer. Math. Soc., 14, 191-196 (1963) · Zbl 0113.09304 · doi:10.2307/2033984
[10] McWilliams, R. D., On iterated w*-sequential closure of cones, Pacific J. Math., 38, 697-715 (1971) · Zbl 0224.46011
[11] Rosenthal, H. P., A characterization of Banach spaces containing l^1, Proc. Nat. Acad. Sci. U.S.A., 71, 2411-2413 (1974) · Zbl 0297.46013 · doi:10.1073/pnas.71.6.2411
[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] Phelps, R., Lectures on Choquet’s Theorem (1966), Princeton, New Jersey: D. van Nostrand Co., Princeton, New Jersey · Zbl 0135.36203
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.