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On dominated extensions in function algebras


Author: J. Globevnik
Journal: Proc. Amer. Math. Soc. 79 (1980), 571-576
MSC: Primary 46J10
DOI: https://doi.org/10.1090/S0002-9939-1980-0572304-0
MathSciNet review: 572304
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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 $ \vert f(s)\vert \leqslant p(s)(s \in F)$ extends to a function $ \tilde f \in A$ satisfying $ \vert\tilde f(z)\vert \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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DOI: https://doi.org/10.1090/S0002-9939-1980-0572304-0
Article copyright: © Copyright 1980 American Mathematical Society

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