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Proceedings of the American Mathematical Society

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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?)

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

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