Countably evaluating homomorphisms on real function algebras

Eva Adam; Peter Biström; Andreas Kriegl

Archivum Mathematicum (1999)

  • Volume: 035, Issue: 2, page 165-192
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Adam, Eva, Biström, Peter, and Kriegl, Andreas. "Countably evaluating homomorphisms on real function algebras." Archivum Mathematicum 035.2 (1999): 165-192. <http://eudml.org/doc/248362>.

@article{Adam1999,
abstract = {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.},
author = {Adam, Eva, Biström, Peter, Kriegl, Andreas},
journal = {Archivum Mathematicum},
keywords = {realcompactness; algebras of smoth functions; countably evaluating homomorphisms; realcompactness; algebras of smooth functions; countably evaluating homomorphisms},
language = {eng},
number = {2},
pages = {165-192},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Countably evaluating homomorphisms on real function algebras},
url = {http://eudml.org/doc/248362},
volume = {035},
year = {1999},
}

TY - JOUR
AU - Adam, Eva
AU - Biström, Peter
AU - Kriegl, Andreas
TI - Countably evaluating homomorphisms on real function algebras
JO - Archivum Mathematicum
PY - 1999
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 035
IS - 2
SP - 165
EP - 192
AB - 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.
LA - eng
KW - realcompactness; algebras of smoth functions; countably evaluating homomorphisms; realcompactness; algebras of smooth functions; countably evaluating homomorphisms
UR - http://eudml.org/doc/248362
ER -

References

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  1. Smoothly realcompact spaces, Thesis, Univ. Vienna 1993. 
  2. A real valued homomorphism on algebras of differentiable functions, Proc. Amer. Math. Soc. 90, 407–411 (1984). Zbl0694.46036MR0929406
  3. C -bounding sets and compactness, Math. Scand. 75, 82–86 (1994). MR1308939
  4. Algebras of real analytic functions; Homomorphisms and bounding sets, Stud. Math. 115, 23–37 (1995). MR1347430
  5. Homomorphisms on C ( E ) and C -bounding sets, Monatsh. Math. 115, 257–266 (1993). MR1233957
  6. Characterizations of the spectra of certain function algebras, Archiv Math. 60, 177–181 (1993). MR1199676
  7. Function algebras on which homomorphisms are point evaluations on sequences, Manuscripta Math. 73, 179–185 (1991). MR1128686
  8. On compactness in locally convex spaces, Math. Z. 195, 365–381 (1987). MR0895307
  9. The weak topology of a Banach space, Trans. Amer. Math. Soc. 101, 1–15 (1961). Zbl0104.08502MR0132375
  10. The three space problem for smooth partitions of unity and C ( K ) -spaces, Math. Ann. 288, 613–625 (1990). MR1081267
  11. Measurability in a Banach space, II, Indiana Univ. Math. J. 28, 559–579 (1979). Zbl0418.46034MR0542944
  12. General topology, Berlin, Haldermann 1989. Zbl0684.54001MR1039321
  13. The dual of every Asplund space admits a projectional resolution of identity, Studia Math. 91, 141–151 (1988). MR0985081
  14. Linear Spaces and Differentiation Theory, Wiley 1988. MR0961256
  15. Homomorphisms on function algebras, Can. J. Math. 46, 734–745 (1994). MR1289057
  16. Rings of continuous functions, Springer 1960. MR0116199
  17. Banach space properties of Ciesielski-Pol’s C ( K ) space, Proc. Amer. Math. Soc. 103, 1087–1093 (1988). MR0954988
  18. M-Ideals in Banach Spaces and Banach Algebras, Lecture notes in Mathematics, 1547. Springer 1993. MR1238713
  19. Locally convex spaces, Teubner 1981. Zbl0466.46001MR0632257
  20. Smoothness and its equivalents in weakly compactly generated Banach spaces, J. Functional Anal. 15, 1–11 (1974). MR0417759
  21. Characters on algebras of smooth functions, Ann. Global Anal. Geom. 7, 85–92 (1989). MR1032327
  22. More smoothly real compact spaces, Proc. Amer. Math. Soc. 117, 467–471 (1993). MR1110545
  23. Banach spaces and topology, in: Handbook of set theoretic topology (ed.: K. Kunen and J.E. Vaughan). North-Holland 1984. Zbl0832.46005MR0776619
  24. Smooth partitions of unity on some non-separable Banach spaces, Studia Math. T.XLVI, 43–51 (1973). MR0339255
  25. Topics in locally convex spaces, North-Holland 1982. Zbl0489.46001MR0671092

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