Geodesic
Multiplicative Functionals on Frechet Algebras with Bases
Canadian journal of mathematics, Tome 29 (1977) no. 2, pp. 270-276

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Husain, T.; Liang, J. Multiplicative Functionals on Frechet Algebras with Bases. Canadian journal of mathematics, Tome 29 (1977) no. 2, pp. 270-276. doi: 10.4153/CJM-1977-028-9
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[1] 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] 2. Michael, E., Locally multiplicatively convex topological algebras, Memoirs, American Math. Soc. 11 (1952). Google Scholar

[3] 3. Schaefer, H. H., Topological vector spaces (MacMillan, New York, 1964). Google Scholar

[4] 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

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