The Radon-Nikodym property in conjugate Banach spaces. (English) Zbl 0318.46056


46G10 Vector-valued measures and integration
46G05 Derivatives of functions in infinite-dimensional spaces
46B99 Normed linear spaces and Banach spaces; Banach lattices
46A20 Duality theory for topological vector spaces
28B05 Vector-valued set functions, measures and integrals
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[1] W. J. Davis and R. R. Phelps, The Radon-Nikodym property and dentable sets in Banach spaces (to appear). · Zbl 0298.46046
[2] M. M. Day, Normed linear spaces, 2nd printing, Ergebnesse der Mathematik und ihrer Grenzgebiete, N. F., Heft 21, Academic Press, New York; Springer-Verlag, Berlin, 1962. MR 26 #2847. · Zbl 0100.10802
[3] J. Diestel, The Radon-Nikodym property and the coincidence of integral and nuclear operators, Rev. Roumaine Math. Pures Appl. 17 (1972), 1611 – 1620. · Zbl 0255.28010
[4] Nelson Dunford and B. J. Pettis, Linear operations on summable functions, Trans. Amer. Math. Soc. 47 (1940), 323 – 392. · Zbl 0023.32902
[5] Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. · Zbl 0084.10402
[6] Alexandre Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. No. 16 (1955), 140 (French). · Zbl 0064.35501
[7] R. C. James, A conjecture about \( {l_1}\) subspaces (to appear).
[8] E. B. Leach and J. H. M. Whitfield, Differentiable functions and rough norms on Banach spaces, Proc. Amer. Math. Soc. 33 (1972), 120 – 126. · Zbl 0236.46051
[9] D. R. Lewis and C. Stegall, Banach spaces whose duals are isomorphic to \?\(_{1}\)(\Gamma ), J. Functional Analysis 12 (1973), 177 – 187. · Zbl 0252.46021
[10] H. Maynard, A geometric characterization of Banach spaces possessing the Radon-Nikodym theorem (to appear).
[11] R. S. Phillips, On weakly compact subsets of a Banach space, Amer. J. Math. 65 (1943), 108 – 136. · Zbl 0063.06212 · doi:10.2307/2371776
[12] James R. Retherford, Basic sequences and the Paley-Wiener criterion, Pacific J. Math. 14 (1964), 1019 – 1027. · Zbl 0182.16502
[13] M. A. Rieffel, Dentable subsets of Banach spaces, with application to a Radon-Nikodým theorem, Functional Analysis (Proc. Conf., Irvine, Calif., 1966) Academic Press, London; Thompson Book Co., Washington, D.C., 1967, pp. 71 – 77.
[14] M. A. Rieffel, The Radon-Nikodym theorem for the Bochner integral, Trans. Amer. Math. Soc. 131 (1968), 466 – 487. · Zbl 0169.46803
[15] J. J. Uhl Jr., A note on the Radon-Nikodym property for Banach spaces, Rev. Roumaine Math. Pures Appl. 17 (1972), 113 – 115. · Zbl 0243.28013
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