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Bounded extensions and characterizations of C(X). (English) Zbl 0449.46031

MSC:

46E15 Banach spaces of continuous, differentiable or analytic functions
46A55 Convex sets in topological linear spaces; Choquet theory
46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators
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References:

[1] Alfsen, E.M.: Compact convex sets and boundary integrals. Ergebnisse der Mathematik57. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0209.42601
[2] Andersen, T.B.: A characterization of metrizable simplexes. J. London Math. Soc. (2)22, 338-344 (1980) · Zbl 0441.46009 · doi:10.1112/jlms/s2-22.2.338
[3] Ellis, A.J., Roy, A.K.: Dilated sets and characterizations of simplexes. Invent. Math.56, 101-108 (1980) · Zbl 0433.46007 · doi:10.1007/BF01392544
[4] Glicksberg, I.: Function algebras with closed restrictions. Proc. Amer. Math. Soc.14, 158-161 (1963) · Zbl 0112.07401 · doi:10.1090/S0002-9939-1963-0143050-2
[5] Hirsberg, B., Lazar, A.J.: Complex Lindenstrauss spaces with extreme points. Trans. Amer. Math. Soc.186, 141-150 (1973) · Zbl 0271.46010 · doi:10.1090/S0002-9947-1973-0333671-7
[6] Rogalski, M.: Caractérisation des simplexes par des propriétés portant sur les faces fermées et sur les ensembles compacts de points extrémaux. Math. Scand.28, 159-181 (1971) · Zbl 0225.46014
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