On Dominated Extensions in Function Algebras

Abstract

The Bishop-Gamelin interpolation theorem asserts that given a compact Hausdorff space K, a closed subspace A of C(K), a positive continuous function p on K and a closed set F c K such that every measure in the annihilator of A vanishes on F, every function/_ G C(F) satisfying \f(s)\ < p(s) (s G F) extends to a function / G A satisfying \f(z)\ < p(z) (z G K). In the paper we consider a special case where the theorem is extended to the situation when the dominating function is nonnegative.