Countably evaluating homomorphisms on real function algebras
Archivum mathematicum, Tome 35 (1999) no. 2, pp. 165-192 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

By studying algebra homomorphisms, which act as point evaluations on each countable subset, we obtain improved results on the question when all algebra homomorphisms are point evaluations.
By studying algebra homomorphisms, which act as point evaluations on each countable subset, we obtain improved results on the question when all algebra homomorphisms are point evaluations.
Classification : 46E25, 46J10, 46J15, 54C35, 54D60
Keywords: realcompactness; algebras of smoth functions; countably evaluating homomorphisms
@article{ARM_1999_35_2_a8,
     author = {Adam, Eva and Bistr\"om, Peter and Kriegl, Andreas},
     title = {Countably evaluating homomorphisms on real function algebras},
     journal = {Archivum mathematicum},
     pages = {165--192},
     year = {1999},
     volume = {35},
     number = {2},
     mrnumber = {1711724},
     zbl = {1050.46025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1999_35_2_a8/}
}
TY  - JOUR
AU  - Adam, Eva
AU  - Biström, Peter
AU  - Kriegl, Andreas
TI  - Countably evaluating homomorphisms on real function algebras
JO  - Archivum mathematicum
PY  - 1999
SP  - 165
EP  - 192
VL  - 35
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ARM_1999_35_2_a8/
LA  - en
ID  - ARM_1999_35_2_a8
ER  - 
%0 Journal Article
%A Adam, Eva
%A Biström, Peter
%A Kriegl, Andreas
%T Countably evaluating homomorphisms on real function algebras
%J Archivum mathematicum
%D 1999
%P 165-192
%V 35
%N 2
%U http://geodesic.mathdoc.fr/item/ARM_1999_35_2_a8/
%G en
%F ARM_1999_35_2_a8
Adam, Eva; Biström, Peter; Kriegl, Andreas. Countably evaluating homomorphisms on real function algebras. Archivum mathematicum, Tome 35 (1999) no. 2, pp. 165-192. http://geodesic.mathdoc.fr/item/ARM_1999_35_2_a8/

[Ad] Adam, E.: Smoothly realcompact spaces. Thesis, Univ. Vienna 1993.

[Ar] Arias-de-Reyna, J.: A real valued homomorphism on algebras of differentiable functions. Proc. Amer. Math. Soc. 90, 407–411 (1984). | MR | Zbl

[BJ] Biström, P., Jaramillo, J.A.: $C^\infty $-bounding sets and compactness. Math. Scand. 75, 82–86 (1994). | MR

[BJL] Biström, P., Jaramillo, J.A., Lindström, M.: Algebras of real analytic functions; Homomorphisms and bounding sets. Stud. Math. 115, 23–37 (1995). | MR

[BL$_1$] Biström, P., Lindström, M.: Homomorphisms on $C^\infty (E)$ and $C^\infty $-bounding sets. Monatsh. Math. 115, 257–266 (1993). | MR

[BL$_2$] Biström, P., Lindström, M.: Characterizations of the spectra of certain function algebras. Archiv Math. 60, 177–181 (1993). | MR

[BBL] Biström, P., Bjon, S., Lindström, M.: Function algebras on which homomorphisms are point evaluations on sequences. Manuscripta Math. 73, 179–185 (1991). | MR

[CO] Cascales, B., Orihuela, J.: On compactness in locally convex spaces. Math. Z. 195, 365–381 (1987). | MR

[C] Corson, H. H.: The weak topology of a Banach space. Trans. Amer. Math. Soc. 101, 1–15 (1961). | MR | Zbl

[DGZ] Deville, R., Godefroy, G., Zizler, V.E.: The three space problem for smooth partitions of unity and $C(K)$-spaces. Math. Ann. 288, 613–625 (1990). | MR

[Ed] Edgar, G.A.: Measurability in a Banach space, II. Indiana Univ. Math. J. 28, 559–579 (1979). | MR | Zbl

[En] Engelking, R.: General topology. Berlin, Haldermann 1989. | MR | Zbl

[FG] Fabian, M., Godefroy, G.: The dual of every Asplund space admits a projectional resolution of identity. Studia Math. 91, 141–151 (1988). | MR

[FK] Frölicher, A., Kriegl, A.: Linear Spaces and Differentiation Theory. Wiley 1988. | MR

[GGJ] Garrido, M.I., Gómez, J., Jaramillo, J.A.: Homomorphisms on function algebras. Can. J. Math. 46, 734–745 (1994). | MR

[GJ] Gillman, L., Jerison, M.: Rings of continuous functions. Springer 1960. | MR

[GPWZ] Godefroy, G., Pelant, J., Whitfield, J.H.M., Zizler, V.E.: Banach space properties of Ciesielski-Pol’s $C(K)$ space. Proc. Amer. Math. Soc. 103, 1087–1093 (1988). | MR

[HWW] Harmand, P., Werner, D., Werner, W.: M-Ideals in Banach Spaces and Banach Algebras. Lecture notes in Mathematics, 1547. Springer 1993. | MR

[J] Jarchow, H.: Locally convex spaces. Teubner 1981. | MR | Zbl

[JZ] John, K., Zizler, V.: Smoothness and its equivalents in weakly compactly generated Banach spaces. J. Functional Anal. 15, 1–11 (1974). | MR

[KMS] Kriegl, A., Michor, P., Schachermayer, W.: Characters on algebras of smooth functions. Ann. Global Anal. Geom. 7, 85–92 (1989). | MR

[KM] Kriegl, A., Michor, P.: More smoothly real compact spaces. Proc. Amer. Math. Soc. 117, 467–471 (1993). | MR

[N] Negrepontis, S.: Banach spaces and topology. in: Handbook of set theoretic topology (ed.: K. Kunen and J.E. Vaughan). North-Holland 1984. | MR | Zbl

[T] Toruńczyk, H.: Smooth partitions of unity on some non-separable Banach spaces. Studia Math. T.XLVI, 43–51 (1973). | MR

[V] Valdivia, M.: Topics in locally convex spaces. North-Holland 1982. | MR | Zbl