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A generalization of the Rudin-Carleson theorem


Author: Per Hag
Journal: Proc. Amer. Math. Soc. 43 (1974), 341-344
MSC: Primary 46E15
DOI: https://doi.org/10.1090/S0002-9939-1974-0338755-1
Erratum: Proc. Amer. Math. Soc. 60 (1976), 377.
MathSciNet review: 0338755
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Abstract: The purpose of this paper is to prove a common generalization of a theorem due to T. W. Gamelin [3] and a theorem due to Z. Semadeni [5]. Both these results are generalizations of E. Bishop's abstract version of the well-known RudinCarleson theorem [2].


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  • [1] E. M. Alfsen and B. Hirsberg, On dominated extensions in linear subspaces of $ {\mathcal{C}_C}(X)$, Preprint Series, Institute of Mathematics, Univ. of Oslo, 1970.
  • [2] E. Bishop, A general Rudin-Carleson theorem, Proc. Amer. Math. Soc. 13 (1962), 140-143. MR 24 #A3293. MR 0133462 (24:A3293)
  • [3] T. W. Gamelin, Uniform algebras, Prentice-Hall, Englewood Cliffs, N.J., 1969. MR 0410387 (53:14137)
  • [4] P. Hag, Restrictions of convex subsets of $ C(X)$, Ph.D. dissertation, University of Michigan, Ann Arbor, Mich., 1972.
  • [5] Z. Semadeni, Simultaneous extensions and projections in spaces of continuous functions, Lecture Notes, University of Aarhus, 1965.

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DOI: https://doi.org/10.1090/S0002-9939-1974-0338755-1
Article copyright: © Copyright 1974 American Mathematical Society

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