Smooth approximations in Banach spaces
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- by J. Vanderwerff
- Proc. Amer. Math. Soc. 115 (1992), 113-120
- DOI: https://doi.org/10.1090/S0002-9939-1992-1081100-8
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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.References
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Bibliographic Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 115 (1992), 113-120
- MSC: Primary 46B20; Secondary 41A30
- DOI: https://doi.org/10.1090/S0002-9939-1992-1081100-8
- MathSciNet review: 1081100