Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On dominated extensions in function algebras

Author: J. Globevnik
Journal: Proc. Amer. Math. Soc. 79 (1980), 571-576
MSC: Primary 46J10
MathSciNet review: 572304
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46J10

Retrieve articles in all journals with MSC: 46J10

Additional Information

Article copyright: © Copyright 1980 American Mathematical Society

American Mathematical Society