Approximation Properties of Vector Valued Functions.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
Pagination or Media Count:
Set theory, Topology, TheoremsWeierstrass theorem, ModulesMathematicsLet M be a closed CX submodule of the space CXE 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 CXE that are extreme in the set of those which annihilate M and have norm at most one are exactly those of the form phig Lgx 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 Mx sub 0all fx sub 0 for f epsilon M. The proof uses various forms of the Weierstrass approximation theorem for modules. Author
- Theoretical Mathematics