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Homomorphisms on Function Algebras

Published online by Cambridge University Press:  20 November 2018

M. I. Garrido ,
J. Gómez Gil  and
J. A. Jaramillo
M. I. Garrido
Affiliation:
Departamento de Matemáticas, Universidad de Extremadura, Avda. Elvas, s/n 06071-Badajoz, Spain
J. Gómez Gil
Affiliation:
Departamento de Análisis Matemático, Universidad Complutense, 28040-Madrid, Spain
J. A. Jaramillo
Affiliation:
Depártamento de Andlisis Matemático, Universidad Complutense, 28040-Madrid, Spain
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Abstract

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Let A be an algebra of continuous real functions on a topological space X. We study when every nonzero algebra homomorphism φ: A → R is given by evaluation at some point of X. In the case that A is the algebra of rational functions (or real-analytic functions, or Cm-functions) on a Banach space, we provide a positive answer for a wide class of spaces, including separable spaces and super-reflexive spaces (with nonmeasurable cardinal).

Keywords

46E2554C40
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 4 , 01 August 1994 , pp. 734 - 745
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Anderson, F. W., Approximation in systems of real-valued continuous functions, Trans. Amer. Math. Soc. 103(1962), 249–271.Google Scholar
2. Arias-de-Reyna, J., A real-valuedhomomorphism on algebras of differentiablefunctions, Proc. Amer. Math. Soc 104(1988), 1054- 1058.Google Scholar
3. Aron, R. M., Compact polynomials and compact differentiable mappings between Banach spaces, Sém. P. Lelong 1974/75, L.N.M. 524, Springer Verlag, 1976, 231- 222.Google Scholar
4. Biström, P., Bjon, S. and Lindström, M., Remarks on homomorphisms on certain subalgebras of C{X), Math. Japon. 36(1991).Google Scholar
5 Biström, P., Homomorphisms on some function algebras, Monatsh. Math. 111(1991), 93- 97.Google Scholar
6. Biström, P., Function algebras on which homomorphisms are point evaluations on sequences, Manuscripta Math. 73(1991), 179- 185.Google Scholar
7. Biström, P. and Lindström, M., Homomorphisms on C∞(E) and C∞-bounding sets, Monatsh. Math. 115 (1993), 257-266.Google Scholar
8. Corson, H. H., The weak topology of a Banach space, Trans. Amer. Math. Soc. 101(1961), 1–15.Google Scholar
9. Diestel, J., Geometry of Banach spaces. Selected topics, L.N.M. 485, Springer Verlag.Google Scholar
10. Edgar, G. A., Measurability in a Banach space, II, Indiana Univ. Math. J. 28(1979), 559-579.Google Scholar
11. Engelking, R., General Topology, Monograf. Math. Warsaw, (1977).Google Scholar
12. Garrido, M. I. and Montalvo, F., Uniform approximation theorems for real-valued continuous functions, Topology Appl. 45(1992), 145–155.Google Scholar
13. Gillman, L. and Jerison, M., Rings of continuous functions, Princeton, New Jersey, 1960.Google Scholar
14. Gómez, J. and Llavona, J. G., Multiplicative functional on function algebras, Rev. Mat. Univ. Complutense Madrid 1(1988), 19–22.Google Scholar
15. Hirschowitz, A., Sur le non-plongementdes variétés analytiques banachiques réeles, C. R. Acad. Sci. Paris 269(1969), 844-846.Google Scholar
16. Jaramillo, J. A., Algebras defunciones continuas y diferenciables. Homomorfismose interpolación, Thesis. Univ. Complutense, Madrid, 1987.Google Scholar
17. Jaramillo, J. A.,Multiplicativejunctionals on algebras of differentiablefunctions, Arch. Math. 58( 1992), 384-387.Google Scholar
18. Jaramillo, J. A. and Llavona, J. G., On the spectrum of Cl b{E), Math. Ann. 287(1990), 531-538.Google Scholar
19. Jech, T., Set Theory, Academic Press, 1978.Google Scholar
20. John, K., Torunczyk, H. and Zizler, V., Uniformly smooth partitions of unity on super reflexive Banach spaces, Studia Math. 70(1981), 129-137.Google Scholar
21. Kriegl, A., Michor, P. and Schachermayer, W., Characters on algebras of smooth functions, Ann. Global Anal. Geom. 7(1989), 85-92.Google Scholar
22. Michael, E. A., Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11(1952).Google Scholar