On dominated extensions in function algebras

Globevnik, J.

doi:10.1090/S0002-9939-1980-0572304-0

On dominated extensions in function algebras
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Proc. Amer. Math. Soc. 79 (1980), 571-576 Request permission

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 $F \subset K$ such that every measure in the annihilator of A vanishes on F, every function $f \in C(F)$ satisfying $|f(s)| \leqslant p(s)(s \in F)$ extends to a function $\tilde f \in A$ satisfying $|\tilde f(z)| \leqslant p(z)(z \in K)$. In the paper we consider a special case where the theorem is extended to the situation when the dominating function is nonnegative.

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