Approximation Properties of Vector Valued Functions.
Abstract
Set theory, Topology, TheoremsWeierstrass theorem, Modules(Mathematics)Let M be a closed C(X) submodule of the space C(X:E) of all bounded continuous functions on the compact space X with values in the normed linear space E. Then, it is shown that the linear functionals phi on C(X:E) that are extreme in the set of those which annihilate M and have norm at most one are exactly those of the form phi(g) = L(g(x sub 0)), where x sub 0 is a point of X and L is an extreme point of the set of functionals of norm one on E that annihilate the subspace M(x sub 0)=(all f(x sub 0) for f epsilon M). The proof uses various forms of the Weierstrass approximation theorem for modules. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1973
- Accession Number
- AD0770738
Entities
People
- R. C. Buck
Organizations
- University of Wisconsin–Madison