Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the duality between smoothability and dentability

Author: Ted Lewis
Journal: Proc. Amer. Math. Soc. 63 (1977), 239-244
MSC: Primary 46B05
MathSciNet review: 0445275
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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 [Enhancements On Off] (What's this?)

  • [1] Michael Edelstein, Concerning dentability, Pacific J. Math. 46 (1973), 111–114. MR 0324378
  • [2] M. Edelstein, Smoothability versus dentability, Comment. Math. Univ. Carolinae 14 (1973), 127–133. MR 0320708
  • [3] Daniel G. Kemp, A note on smoothability in Banach spaces, Math. Ann. 218 (1975), no. 3, 211–217. MR 0399808
  • [4] 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
  • [5] Francis Sullivan, Dentability, smoothability and stronger properties in Banach spaces, Indiana Univ. Math. J. 26 (1977), no. 3, 545–553. MR 0438088
  • [6] R. Anantharaman and J. H. M. Whitfield, Smoothability Banach spaces, Notices Amer. Math. Soc. 23 (1976), A-535. Abstract #737-46-3.

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Keywords: Smoothability, dentability, Gâteaux differentiability
Article copyright: © Copyright 1977 American Mathematical Society