Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Restrictions of convex subsets of $ C(X)$


Author: Per Hag
Journal: Trans. Amer. Math. Soc. 233 (1977), 283-294
MSC: Primary 46E10
DOI: https://doi.org/10.1090/S0002-9947-1977-0467264-1
MathSciNet review: 0467264
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The main result of this paper is a theorem giving a measure-theoretic condition which is necessary and sufficient for a closed convex subset S of $ C(X)$ to have the so-called bounded extension property with respect to a closed subset F of X. This theorem generalizes well-known results on closed subspaces by Bishop, Gamelin and Semadeni.


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

  • [1] E. M. Alfsen and B. Hirsberg, On dominated extensions in linear subspaces of $ {\mathcal{C}_{\mathbf{C}}}(X)$, Preprint series, Inst. of Math., Univ. of Oslo, 1970.
  • [2] E. L. Arenson, On the closure of the image of a convex set, Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 22 (1971), 171-174. (Russian) MR 45 #871. MR 0291780 (45:871)
  • [3] E. Bishop, A general Rudin-Carleson theorem, Proc. Amer. Math. Soc. 13 (1962), 140-143. MR 24 #A3293. MR 0133462 (24:A3293)
  • [4] N. Dunford and J. T. Schwartz, Linear operators. Vol. I, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302.
  • [5] T. W. Gamelin, Restrictions of subspaces of $ C(X)$, Trans. Amer. Math. Soc. 112 (1964), 278-286. MR 28 #5331. MR 0162132 (28:5331)
  • [6] -, Uniform algebras, Prentice-Hall, Englewood Cliffs, N.J., 1969. MR 0410387 (53:14137)
  • [7] I. Glicksberg, Measures orthogonal to algebras and sets of antisymmetry, Trans. Amer. Math. Soc. 105 (1962), 415-435. MR 30 #4164. MR 0173957 (30:4164)
  • [8] P. Hag, Restrictions of convex subsets of $ C(X)$, Ph. D. dissertation, Univ. of Michigan, 1972.
  • [9] -, A generalization of the Rudin-Carleson theorem, Proc. Amer. Math. Soc. 43 (1974), 341-344. MR 49 #3519. MR 0338755 (49:3519)
  • [10] -, Erratum to ``A generalization of the Rudin-Carleson theorem", Proc. Amer. Math. Soc. 60 (1976), 377. MR 0415325 (54:3414)
  • [11] E. Michael and A. Pełczyński, A linear extension theorem, Illinois J. Math. 11 (1967), 563-579. MR 36 #671. MR 0217582 (36:671)
  • [12] H. L. Royden, Real analysis, Macmillan, New York, 1968. MR 0151555 (27:1540)
  • [13] Z. Semadeni, Simultaneous extensions and projections in spaces of continuous functions Lecture Notes, Univ. of Aarhus, 1965.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46E10

Retrieve articles in all journals with MSC: 46E10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0467264-1
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society