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Multiplicative Functionals on Frechet Algebras with Bases

Published online by Cambridge University Press:  20 November 2018

T. Husain  and
J. Liang
T. Husain
Affiliation:
McMaster University, Hamilton, Ontario
J. Liang
Affiliation:
McMaster University, Hamilton, Ontario
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Abstract

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Let A denote a complex (or real) Fréchet algebra (i.e. a complete metrizable locally m-convex algebra, see [2] or [3]). It is known [2] that the topology of such an algebra can be defined by an increasing sequence [qn] (i.e. qn(x) ≦ qn+i(x) for all x £ A and n ≧ 1) of submultiplicative (i.e. qn(xy) ≦ qn(x)qn(y) for all x, 3/ Ç ^4 and for each n ≧ I) seminorms.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 2 , 01 April 1977 , pp. 270 - 276
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Husain, T. and S-B. Ng, On continuity of algebra homomorphisms and uniqueness of metric topology, Math. Z. 139 (1974), 1–4.Google Scholar
2. Michael, E., Locally multiplicatively convex topological algebras, Memoirs, American Math. Soc. 11 (1952).Google Scholar
3. Schaefer, H. H., Topological vector spaces (MacMillan, New York, 1964).Google Scholar
4. Liang, J., Relations among coefficients, seminorms and identities of Fréchet algebras with Schauder bases, Soo-Chow J. of Math, and Natural Sciences 1 (1975), 59–65.Google Scholar