Smooth approximations in Banach spaces

Vanderwerff, J.

doi:10.1090/S0002-9939-1992-1081100-8

Smooth approximations in Banach spaces
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by J. Vanderwerff PDF

Proc. Amer. Math. Soc. 115 (1992), 113-120 Request permission

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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