Fréchet algebra
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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 on the complex plane C, or to the algebra Hol(C) of holomorphic functions on C, both equipped with the topology of uniform convergence on compact sets. Perhaps the most famous, still open problem of the theory of topological algebras is whether any linear-multiplicative functional on a Frechet algebra is continuous.
