Vol. 53, No. 1, 1974

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ISSN: 0030-8730
Approximation properties of vector valued functions

R. Creighton Buck

Vol. 53 (1974), No. 1, 85–94

There are several analogues of the Weierstrass approximation theorem that characterize the uniform closure of a C[X] submodule of the space C[X : E] of bounded continuous E-valued functions on a compact space X. In this paper, a strong form of such a theorem is obtained which is then applied to yield a characterization of all the functionals ϕ in the dual of C[X : E] that are extreme among those of unit norm that vanish on an arbitrary chosen . Each is determined by a point x0 X and a unit functional L that is extreme in the annihilator of a closed subspace M E.

Mathematical Subject Classification 2000
Primary: 46E40
Received: 13 June 1973
Published: 1 July 1974
R. Creighton Buck