On the ideal structure of algebras of LMC-algebra valued functions

Jorma Arhippainen

Studia Mathematica (1992)

  • Volume: 101, Issue: 3, page 311-318
  • ISSN: 0039-3223

Abstract

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Let X be a completely regular topological space and A a commutative locally m-convex algebra. We give a description of all closed and in particular closed maximal ideals of the algebra C(X,A) (= all continuous A-valued functions defined on X). The topology on C(X,A) is defined by a certain family of seminorms. The compact-open topology of C(X,A) is a special case of this topology.

How to cite

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Arhippainen, Jorma. "On the ideal structure of algebras of LMC-algebra valued functions." Studia Mathematica 101.3 (1992): 311-318. <http://eudml.org/doc/215908>.

@article{Arhippainen1992,
abstract = {Let X be a completely regular topological space and A a commutative locally m-convex algebra. We give a description of all closed and in particular closed maximal ideals of the algebra C(X,A) (= all continuous A-valued functions defined on X). The topology on C(X,A) is defined by a certain family of seminorms. The compact-open topology of C(X,A) is a special case of this topology.},
author = {Arhippainen, Jorma},
journal = {Studia Mathematica},
keywords = {commutative locally -convex algebra; closed maximal ideals; compact- open topology},
language = {eng},
number = {3},
pages = {311-318},
title = {On the ideal structure of algebras of LMC-algebra valued functions},
url = {http://eudml.org/doc/215908},
volume = {101},
year = {1992},
}

TY - JOUR
AU - Arhippainen, Jorma
TI - On the ideal structure of algebras of LMC-algebra valued functions
JO - Studia Mathematica
PY - 1992
VL - 101
IS - 3
SP - 311
EP - 318
AB - Let X be a completely regular topological space and A a commutative locally m-convex algebra. We give a description of all closed and in particular closed maximal ideals of the algebra C(X,A) (= all continuous A-valued functions defined on X). The topology on C(X,A) is defined by a certain family of seminorms. The compact-open topology of C(X,A) is a special case of this topology.
LA - eng
KW - commutative locally -convex algebra; closed maximal ideals; compact- open topology
UR - http://eudml.org/doc/215908
ER -

References

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  10. [10] W. Hery, Maximal ideals in algebras of topological algebra valued functions, Pacific J. Math. 65 (1976), 365-373. Zbl0315.46048
  11. [11] A. Mallios, Heredity of tensor products of topological algebras, Math. Ann. 162 (1966), 246-257. Zbl0139.07503
  12. [12] A. Mallios, Topological Algebras. Selected Topics, Elsevier, New York 1986. 
  13. [13] E. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1952). Zbl0047.35502
  14. [14] L. Nachbin, Elements of Approximation Theory, Van Nostrand, Princeton, N.J., 1967. Zbl0173.41403
  15. [15] J. Prolla, Approximation of Vector-Valued Functions, North-Holland, Amsterdam 1977. 
  16. [16] J. Prolla, On the spectra of non-Archimedean function algebras, in: Lecture Notes in Math. 843, Springer, New York 1980, 547-560. 
  17. [17] J. Prolla, Topological algebras of vector-valued continuous functions, in: Math. Anal. and Applic., Part B, Adv. Math. Suppl. Stud. Vol. 7B, Academic Press, 1981, 727-740. 

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