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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Smooth approximations in Banach spaces


Author: J. Vanderwerff
Journal: Proc. Amer. Math. Soc. 115 (1992), 113-120
MSC: Primary 46B20; Secondary 41A30
MathSciNet review: 1081100
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Abstract: A Banach space that has a locally uniformly convex (LUC) norm whose dual is also LUC is shown to admit $ {C^1}$-smooth partitions of unity. It is also established that there is a norm on a Hubert space with Lipschitz derivative that cannot be approximated uniformly on bounded sets by functions with uniformly continuous second derivative.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1081100-8
PII: S 0002-9939(1992)1081100-8
Article copyright: © Copyright 1992 American Mathematical Society