Vol. 53, No. 1, 1974

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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