Smooth Approximations in Banach Spaces

J. Vanderwerff
1992 Proceedings of the American Mathematical Society  
A Banach space that has a locally uniformly convex (LUC) norm whose dual is also LUC is shown to admit Cl -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.
doi:10.2307/2159572 fatcat:bgkjizupabh77lvjpjp2inadrm