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# Accession Number:

## AD0770738

# Title:

## Approximation Properties of Vector Valued Functions.

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

# 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

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#