Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1977-0445275-5
MathSciNet review: 0445275
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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] M. Edelstein, Concerning dentability, Pacific J. Math. 46 (1973), 111-114. MR 48 #2730. MR 0324378 (48:2730)
  • [2] -, Smoothability versus dentability, Comment. Math. Univ. Carolinae 14 (1973), 127-133. MR 47 #9243. MR 0320708 (47:9243)
  • [3] D. C. Kemp, A note on smoothability in Banach spaces, Math. Ann. 218 (1975), 211-217. MR 0399808 (53:3650)
  • [4] M. A. Rieffel, Dentable subsets of Banach spaces, with applications to a Radon-Nikodým theorem, Functional Analysis (Proc. Conf., Irvine, Calif., 1966), Academic Press, London; Thompson, Washington, D. C., 1967, pp. 71-77. MR 36 #5668. MR 0222618 (36:5668)
  • [5] F. Sullivan, Dentability, smoothability and stronger properties in Banach spaces, (preprint). MR 0438088 (55:11007)
  • [6] R. Anantharaman and J. H. M. Whitfield, Smoothability Banach spaces, Notices Amer. Math. Soc. 23 (1976), A-535. Abstract #737-46-3.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46B05

Retrieve articles in all journals with MSC: 46B05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0445275-5
Keywords: Smoothability, dentability, Gâteaux differentiability
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society