Fréchet algebra

Fréchet algebra

In mathematics, a Fréchet algebra is a topological algebra, in which the topology is given by a countable family of submultiplicative seminorms:

:"p"(fg) ≤ "p"(f)"p"(g),

and the algebra is complete.

For example, A can be equal to C(C), the algebra of all continuous functions onthe complex plane C, or to the algebra Hol(C) of holomorphic functions on C, bothequipped with the topology of uniform convergence on compact sets. Perhaps themost famous, still open problem of the theory of topological algebras is whether anylinear-multiplicative functional on a Frechet algebra is continuous.

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