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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
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Abstract

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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

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