Accession Number:

AD0770738

Title:

Approximation Properties of Vector Valued Functions.

Descriptive Note:

Technical summary rept.,

Corporate Author:

WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

• Buck,R. C.

Report Date:

1973-10-01

Pagination or Media Count:

19.0

Abstract:

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

Descriptors:

• *APPROXIMATION(MATHEMATICS)
• *FUNCTIONS(MATHEMATICS)
• SET THEORY
• TOPOLOGY
• THEOREMS

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE