The abstract Dirichlet problem for continuous vector-valued functions

Abstract

Let X be a simplex with the set of extreme points being Lindelof. We show that a continuous bounded mapping defined on with values in a Fr,chet space F can be extended to a mapping that is a pointwise limit of a bounded sequence of affine continuous mappings from X to F.

Keywords

• Simplex
• Vector-valued Baire function
• Strongly affine function
• Pettis integral