Banach spaces which always contain supremum-attaining elements
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- by Peter D. Morris PDF
- Proc. Amer. Math. Soc. 83 (1981), 496-498 Request permission
Abstract:
It is proved that if a weakly compactly generated Banach space $X$ has the property that, for every closed, bounded convex subset $K$ of ${X^ * }$, there exists a nonzero element of $X$ which attains its supremum on $K$, then $X$ contains no copy of ${l^1}$.References
-
R. Bourgin, Notes on the Radon-Nikodym property (to appear).
- Joseph Diestel, Geometry of Banach spaces—selected topics, Lecture Notes in Mathematics, Vol. 485, Springer-Verlag, Berlin-New York, 1975. MR 0461094
- 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
- I. Namioka and R. R. Phelps, Banach spaces which are Asplund spaces, Duke Math. J. 42 (1975), no. 4, 735–750. MR 390721
- A. Pełczyński, On $C(S)$-subspaces of separable Banach spaces, Studia Math. 31 (1968), 513–522. MR 234261, DOI 10.4064/sm-31-5-513-522 J. Rainwater, Univ. of Washington Seminar Notes, Fall 1976.
- Charles Stegall, The duality between Asplund spaces and spaces with the Radon-Nikodým property, Israel J. Math. 29 (1978), no. 4, 408–412. MR 493268, DOI 10.1007/BF02761178
- 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
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 496-498
- MSC: Primary 46B20
- DOI: https://doi.org/10.1090/S0002-9939-1981-0627677-8
- MathSciNet review: 627677