A characterization of maximal regular ideals in lmc algebras

Maria Fragoulopoulou

Studia Mathematica (1992)

  • Volume: 103, Issue: 1, page 41-49
  • ISSN: 0039-3223

Abstract

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A question of Warner and Whitley concerning a nonunital version of the Gleason-Kahane-Żelazko theorem is considered in the context of nonnormed topological algebras. Among other things it is shown that a closed hyperplane M of a commutative symmetric F*-algebra E with Lindelöf Gel'fand space is a maximal regular ideal iff each element of M belongs to some closed maximal regular ideal of E.

How to cite

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Fragoulopoulou, Maria. "A characterization of maximal regular ideals in lmc algebras." Studia Mathematica 103.1 (1992): 41-49. <http://eudml.org/doc/215934>.

@article{Fragoulopoulou1992,
abstract = {A question of Warner and Whitley concerning a nonunital version of the Gleason-Kahane-Żelazko theorem is considered in the context of nonnormed topological algebras. Among other things it is shown that a closed hyperplane M of a commutative symmetric F*-algebra E with Lindelöf Gel'fand space is a maximal regular ideal iff each element of M belongs to some closed maximal regular ideal of E.},
author = {Fragoulopoulou, Maria},
journal = {Studia Mathematica},
keywords = {symmetric lmc*-algebra; LFQ-algebra; maximal ideal space; Lindelöf space; nonunital version of the Gleason-Kahane-Żelazko theorem; nonnormed topological algebras; commutative symmetric -algebra; Lindelöf- Gel’fand space; maximal regular ideal},
language = {eng},
number = {1},
pages = {41-49},
title = {A characterization of maximal regular ideals in lmc algebras},
url = {http://eudml.org/doc/215934},
volume = {103},
year = {1992},
}

TY - JOUR
AU - Fragoulopoulou, Maria
TI - A characterization of maximal regular ideals in lmc algebras
JO - Studia Mathematica
PY - 1992
VL - 103
IS - 1
SP - 41
EP - 49
AB - A question of Warner and Whitley concerning a nonunital version of the Gleason-Kahane-Żelazko theorem is considered in the context of nonnormed topological algebras. Among other things it is shown that a closed hyperplane M of a commutative symmetric F*-algebra E with Lindelöf Gel'fand space is a maximal regular ideal iff each element of M belongs to some closed maximal regular ideal of E.
LA - eng
KW - symmetric lmc*-algebra; LFQ-algebra; maximal ideal space; Lindelöf space; nonunital version of the Gleason-Kahane-Żelazko theorem; nonnormed topological algebras; commutative symmetric -algebra; Lindelöf- Gel’fand space; maximal regular ideal
UR - http://eudml.org/doc/215934
ER -

References

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  1. [1] R. S. Doran and J. Wichmann, Approximate Identities and Factorization in Banach Modules, Springer, Berlin 1979. Zbl0418.46039
  2. [2] M. Fragoulopoulou, An Introduction to the Representation Theory of Topological *-Algebras, Schriftenreihe Math. Inst. Univ. Münster 48, 1988. 
  3. [3] M. Fragoulopoulou, Symmetric topological *-algebras, II, in: Trends in Functional Analysis and Approximation Theory, Proc. Maratea 1989, 279-288. 
  4. [4] M. Fragoulopoulou, Uniqueness of topology for semisimple LFQ-algebras, Proc. Amer. Math. Soc., to appear. Zbl0784.46031
  5. [5] A. Gleason, A characterization of maximal ideals, J. Analyse Math. 19 (1967), 171-172. Zbl0148.37502
  6. [6] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. 1, Springer, Berlin 1963. Zbl0115.10603
  7. [7] J. Horváth, Topological Vector Spaces and Distributions, Vol. I, Addison-Wesley, Reading, Mass., 1966. 
  8. [8] H. Jarchow, Locally Convex Spaces, Teubner, Stuttgart 1981. 
  9. [9] J. P. Kahane and W. Żelazko, A characterization of maximal ideals in commutative Banach algebras, Studia Math. 29 (1968), 339-343. Zbl0155.45803
  10. [10] J. L. Kelley, General Topology, Springer, New York 1955. Zbl0066.16604
  11. [11] G. Lumer, Bochner's theorem, states and the Fourier transforms of measures, Studia Math. 46 (1973), 135-140. Zbl0286.43008
  12. [12] A. Mallios, Topological Algebras. Selected Topics, North-Holland, Amsterdam 1966. 
  13. [13] G. Maltese and R. Wille-Fier, A characterization of homomorphisms in certain Banach involution algebras, Studia Math. 89 (1988),133-143. Zbl0756.46024
  14. [14] E. A. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1952) (reprinted 1968). Zbl0047.35502
  15. [15] M. Roitman and Y. Sternfeld, When is a linear functional multiplicative?, Trans. Amer. Math. Soc. 267 (1981), 111-124. Zbl0474.46039
  16. [16] C. R. Warner and R. Whitley, A characterization of regular maximal ideals, Pacific J. Math. 30 (1969), 277-281. Zbl0176.43903
  17. [17] W. Żelazko, A characterization of multiplicative linear functionals in complex Banach algebras, Studia Math. 30 (1968), 83-85. Zbl0162.18504
  18. [18] W. Żelazko, On multiplicative linear functionals, Colloq. Math. 28 (1973), 251-253. Zbl0238.46049

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