On the duality between smoothability and dentability
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- by Ted Lewis PDF
- Proc. Amer. Math. Soc. 63 (1977), 239-244 Request permission
Abstract:
By renorming ${l_1}$ with an equivalent dual norm it is shown that smoothability of the unit ball of a conjugate Banach space ${E^\ast }$ does not imply dentability of the unit ball of either E or ${E^{\ast \ast }}$. It is also shown that the unit ball may be smoothable yet fail to be smooth at any point.References
- Michael Edelstein, Concerning dentability, Pacific J. Math. 46 (1973), 111–114. MR 324378
- M. Edelstein, Smoothability versus dentability, Comment. Math. Univ. Carolinae 14 (1973), 127–133. MR 320708
- Daniel C. Kemp, A note on smoothability in Banach spaces, Math. Ann. 218 (1975), no. 3, 211–217. MR 399808, DOI 10.1007/BF01349695
- 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
- Francis Sullivan, Dentability, smoothability and stronger properties in Banach spaces, Indiana Univ. Math. J. 26 (1977), no. 3, 545–553. MR 438088, DOI 10.1512/iumj.1977.26.26042 R. Anantharaman and J. H. M. Whitfield, Smoothability Banach spaces, Notices Amer. Math. Soc. 23 (1976), A-535. Abstract #737-46-3.
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 63 (1977), 239-244
- MSC: Primary 46B05
- DOI: https://doi.org/10.1090/S0002-9939-1977-0445275-5
- MathSciNet review: 0445275