ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 46 Fry, Robb, University of Northern British Columbia, Canada Smooth Bump Functions on Banach Spaces A C^{k}-smooth bump function on a Banach space, is a C^{k}-smooth, realvalued function with bounded, non-empty support. We show that a weakly countably determined Banach space (which includes separable and reflexive spaces) admits a C^{k}-smooth bumb function whenever each of its separable subspaces does. This allows us to prove that a Banach space X admits a norm with modulus of smoothness of power type 2 iff X has the Radon Nikodym property and admits a contnuous, twice Gâteaux differentiable bumb function, and in addition, that for K a scattered, Eberlein compact, C(K) admits a C^{∞}-smooth bumb function.