A generalization of the Rudin-Carleson theorem

Author:
Per Hag

Journal:
Proc. Amer. Math. Soc. **43** (1974), 341-344

MSC:
Primary 46E15

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**].

**[1]**E. M. Alfsen and B. Hirsberg,*On dominated extensions in linear subspaces of*, Preprint Series, Institute of Mathematics, Univ. of Oslo, 1970.**[2]**Errett Bishop,*A general Rudin-Carleson theorem*, Proc. Amer. Math. Soc.**13**(1962), 140–143. MR**0133462**, 10.1090/S0002-9939-1962-0133462-4**[3]**Theodore W. Gamelin,*Uniform algebras*, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1969. MR**0410387****[4]**P. Hag,*Restrictions of convex subsets of*, 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:
http://dx.doi.org/10.1090/S0002-9939-1974-0338755-1

Article copyright:
© Copyright 1974
American Mathematical Society