The Radon-Nikodym property in conjugate Banach spaces
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- by Charles Stegall
- Trans. Amer. Math. Soc. 206 (1975), 213-223
- DOI: https://doi.org/10.1090/S0002-9947-1975-0374381-1
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Abstract:
We characterize conjugate Banach spaces ${X^\ast }$ having the Radon-Nikodym Property as those spaces such that any separable subspace of $X$ has a separable conjugate. Several applications are given.References
- W. J. Davis and R. R. Phelps, The Radon-Nikodym property and dentable sets in Banach spaces (to appear).
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.
- J. Diestel, The Radon-Nikodym property and the coincidence of integral and nuclear operators, Rev. Roumaine Math. Pures Appl. 17 (1972), 1611–1620. MR 333728
- Nelson Dunford and B. J. Pettis, Linear operations on summable functions, Trans. Amer. Math. Soc. 47 (1940), 323–392. MR 2020, DOI 10.1090/S0002-9947-1940-0002020-4
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- Alexandre Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955), Chapter 1: 196 pp.; Chapter 2: 140 (French). MR 75539 R. C. James, A conjecture about ${l_1}$ subspaces (to appear).
- E. B. Leach and J. H. M. Whitfield, Differentiable functions and rough norms on Banach spaces, Proc. Amer. Math. Soc. 33 (1972), 120–126. MR 293394, DOI 10.1090/S0002-9939-1972-0293394-4
- D. R. Lewis and C. Stegall, Banach spaces whose duals are isomorphic to $l_{1}(\Gamma )$, J. Functional Analysis 12 (1973), 177–187. MR 0342987, DOI 10.1016/0022-1236(73)90022-0 H. Maynard, A geometric characterization of Banach spaces possessing the Radon-Nikodym theorem (to appear).
- R. S. Phillips, On weakly compact subsets of a Banach space, Amer. J. Math. 65 (1943), 108–136. MR 7938, DOI 10.2307/2371776
- James R. Retherford, Basic sequences and the Paley-Wiener criterion, Pacific J. Math. 14 (1964), 1019–1027. MR 170195
- 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. MR 0222618
- M. A. Rieffel, The Radon-Nikodym theorem for the Bochner integral, Trans. Amer. Math. Soc. 131 (1968), 466–487. MR 222245, DOI 10.1090/S0002-9947-1968-0222245-2
- J. J. Uhl Jr., A note on the Radon-Nikodym property for Banach spaces, Rev. Roumaine Math. Pures Appl. 17 (1972), 113–115. MR 482100
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 206 (1975), 213-223
- MSC: Primary 28A45; Secondary 46B99, 46G10
- DOI: https://doi.org/10.1090/S0002-9947-1975-0374381-1
- MathSciNet review: 0374381