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

Studia Mathematica (1992)

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

## Access Full Article

top## Abstract

top## How to cite

topArhippainen, 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

top- [1] M. Abel, The description of linear multiplicative functionals in the algebras of continuous functions, Uchen. Zap. Tartusk. Univ. 430 (1977), 14-21.
- [2] M. Abel, Description of closed ideals in algebras of continuous vector-valued functions, Math. Notes 30 (5) (1981), 887-892. Zbl0494.46053
- [3] J. Arhippainen, On the ideal structure and approximation properties of algebras of continuous B*-algebra valued functions, Acta Univ. Oulu. Ser. A 187 (1987). Zbl0637.46057
- [4] E. Beckenstein, L. Narici and S. Suffel, Topological Algebras, North-Holland, New York 1977.
- [5] W. Dietrich, The maximal ideal space of the topological algebra C(X,E), Math. Ann. 183 (1969), 201-212. Zbl0169.17703
- [6] W. Dietrich, Function algebras on completely regular spaces, Diss. Northwestern Univ., Evanston, Ill., 1971.
- [7] J. Dugundji, Topology, Allyn and Bacon, Boston 1966.
- [8] W. Hery, Rings of continuous Banach algebra-valued functions, Doct. Diss. Abstrs 45, Polytech. Inst. of New York, 1974.
- [9] W. Hery, Maximal ideals in algebras of continuous C(S) valued functions, Atti Acad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 58 (2) (1975), 195-199.
- [10] W. Hery, Maximal ideals in algebras of topological algebra valued functions, Pacific J. Math. 65 (1976), 365-373. Zbl0315.46048
- [11] A. Mallios, Heredity of tensor products of topological algebras, Math. Ann. 162 (1966), 246-257. Zbl0139.07503
- [12] A. Mallios, Topological Algebras. Selected Topics, Elsevier, New York 1986.
- [13] E. Michael, Locally multiplicatively-convex topological algebras, Mem. Amer. Math. Soc. 11 (1952). Zbl0047.35502
- [14] L. Nachbin, Elements of Approximation Theory, Van Nostrand, Princeton, N.J., 1967. Zbl0173.41403
- [15] J. Prolla, Approximation of Vector-Valued Functions, North-Holland, Amsterdam 1977.
- [16] J. Prolla, On the spectra of non-Archimedean function algebras, in: Lecture Notes in Math. 843, Springer, New York 1980, 547-560.
- [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.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.