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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
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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.


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