Published online by Cambridge University Press: 20 November 2018
Let A denote a complex (or real) Fréchet algebra (i.e. a complete metrizable locally m-convex algebra, see  or ). It is known  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.