Bounded extension property and 𝑝-sets

Hag, Per

doi:10.1090/S0002-9939-1980-0550503-1

Bounded extension property and $p$-sets
HTML articles powered by AMS MathViewer

by Per Hag

Proc. Amer. Math. Soc. 78 (1980), 235-238

DOI: https://doi.org/10.1090/S0002-9939-1980-0550503-1

PDF | Request permission

Abstract:

The main result of this paper is a theorem which asserts that a closed subset of the compact Hausdorff space X is a p-set for a uniform algebra A on X if and only if $S = \{ f \in A;\operatorname {Re} f \geqslant 0\}$ has the so-called bounded extension property with respect to F. Similar results have been obtained by Bishop, Gamelin, Semadeni and the author.

References

The closedness of the image of a convex set, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 22 (1971), 171–174 (Russian). MR 0291780
Errett Bishop, A general Rudin-Carleson theorem, Proc. Amer. Math. Soc. 13 (1962), 140–143. MR 133462, DOI 10.1090/S0002-9939-1962-0133462-4
T. W. Gamelin, Restrictions of subspaces of $C(X)$, Trans. Amer. Math. Soc. 112 (1964), 278–286. MR 162132, DOI 10.1090/S0002-9947-1964-0162132-8
Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969. MR 0410387
J. Globevnik, Analytic extensions and selections, Trans. Amer. Math. Soc. 254 (1979), 171–177. MR 539913, DOI 10.1090/S0002-9947-1979-0539913-2
Per Hag, Restrictions of convex subsets of $C(X)$, Trans. Amer. Math. Soc. 233 (1977), 283–294. MR 467264, DOI 10.1090/S0002-9947-1977-0467264-1
E. Michael and A. Pełczyński, A linear extension theorem, Illinois J. Math. 11 (1967), 563–579. MR 217582, DOI 10.1215/ijm/1256054447

Simultaneous extensions and projections in spaces of continuous functions