Peak sets for the real part of a function algebra
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- by Eggert Briem PDF
- Proc. Amer. Math. Soc. 85 (1982), 77-78 Request permission
Abstract:
We show that if $A$ is a function algebra with the property that every peak set for re $A$ is an interpolation set for $A$ then $A = C(X)$.References
- L. Asimow and A. J. Ellis, Convexity theory and its applications in functional analysis, London Mathematical Society Monographs, vol. 16, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1980. MR 623459
- Eggert Briem, Split faces associated with function algebras, J. London Math. Soc. (2) 9 (1974/75), 446–450. MR 365149, DOI 10.1112/jlms/s2-9.3.446
- Eggert Briem, A characterization of simplexes by parallel faces, Bull. London Math. Soc. 12 (1980), no. 1, 55–59. MR 565485, DOI 10.1112/blms/12.1.55
- A. J. Ellis, On split faces and function algebras, Math. Ann. 195 (1972), 159–166. MR 291812, DOI 10.1007/BF01419623
- Alan J. Ellis, On facially continuous functions in function algebras, J. London Math. Soc. (2) 5 (1972), 561–564. MR 318892, DOI 10.1112/jlms/s2-5.3.561
- Alan J. Ellis, Central decompositions and the essential set for the space $A(K)$, Proc. London Math. Soc. (3) 26 (1973), 564–576. MR 315399, DOI 10.1112/plms/s3-26.3.564
- I. Glicksberg, Function algebras with closed restrictions, Proc. Amer. Math. Soc. 14 (1963), 158–161. MR 143050, DOI 10.1090/S0002-9939-1963-0143050-2
- Bent Hirsberg, $M$-ideals in complex function spaces and algebras, Israel J. Math. 12 (1972), 133–146. MR 315451, DOI 10.1007/BF02764658
- B. Hirsberg and A. J. Lazar, Complex Lindenstrauss spaces with extreme points, Trans. Amer. Math. Soc. 186 (1973), 141–150. MR 333671, DOI 10.1090/S0002-9947-1973-0333671-7
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 85 (1982), 77-78
- MSC: Primary 46J10; Secondary 46A55
- DOI: https://doi.org/10.1090/S0002-9939-1982-0647902-8
- MathSciNet review: 647902