Vol. 42, No. 1, 1972

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On Banach space valued extensions from split faces

Tage Bai Andersen

Vol. 42 (1972), No. 1, 1–9

The object of this note is the following theorem: Suppose a is a continuous affine map from a closed split face F of a compact convex set K with values in a Banach space B enjoying the approximation property. Suppose also that p is a strictly positive lower semi-continuous concave function on K such that a(k)p(k) for all k in F. Then a admits a continuous affine extension ã to K into B such that ã(k)p(k) for all k in K.

Mathematical Subject Classification 2000
Primary: 46E15
Secondary: 46B99, 46A05
Received: 30 March 1971
Published: 1 July 1972
Tage Bai Andersen