Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T00:56:07.810Z Has data issue: false hasContentIssue false
  • English
  • Français

A class of factorable topological algebras

Published online by Cambridge University Press:  20 January 2009

E. Ansari-Piri
E. Ansari-Piri
Affiliation:
Department of Pure Mathematics, Faculty of Science, Guilan University, P.O. Box 451, Rasht, Iran
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The famous Cohen factorization theorem, which says that every Banach algebra with bounded approximate identity factors, has already been generalized to locally convex algebras with what may be termed “uniformly bounded approximate identities”. Here we introduce a new notion, that of fundamentality generalizing both local boundedness and local convexity, and we show that a fundamental Fréchet algebra with uniformly bounded approximate identity factors. Fundamentality is a topological vector space property rather than an algebra property. We exhibit some non-fundamental topological vector space and give a necessary condition for Orlicz space to be fundamental.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 33 , Issue 1 , February 1990 , pp. 53 - 59
Copyright
Copyright © Edinburgh Mathematical Society 1990

References

REFERENCES

1.Bonsall, F. F. and Duncan, J., Complete Normed Algebras (Springer-Verlag, Berlin, 1973).CrossRefGoogle Scholar
2.Craw, I. G., Factorization in Fréchet-algebras, J. London Math. Soc. 44 (1969), 607–611.CrossRefGoogle Scholar
3.Dixon, P. G., Automatic continuity of positive functionals on topological involution algebras, Bull. Austral. Math. Soc. 23 (1981), 265–281.CrossRefGoogle Scholar
4.Doran, R. S. and Wichmann, J., Approximate Identities and Factorization in Banach Modules (Lecture Notes in Mathematics 768, Springer-Verlag, Berlin, 1979).CrossRefGoogle Scholar
5.Kalton, N. J., Peck, N. T. and Roberts, James W., An F-space Sampler (London Mathematical Society Lecture Note series, 89, Cambridge University Press, Cambridge, 1984).Google Scholar
6.Mallios, A., Topological Algebras, Selected Topics (Mathematical Studies, 124, North-Holland, Amsterdam, 1986).CrossRefGoogle Scholar
7.Robertson, A. P. and Robertson, Wendy, Topological Vector Spaces (Cambridge University Press, Cambridge, Second Edition 1973).Google Scholar
8.Summers, M. K., Factorization in Fréchet modules, J. London Math. Soc. (2), 5 (1972), 243–248.CrossRefGoogle Scholar
9.żelazko, W., Banach Algebras (PWN-Polish Scientific Publishers, Warszawa 1973).Google Scholar