CommutativeF-algebras
Melvin A. Rosenfeld · Pacific Journal of Mathematics · 1966
We extend several theorems for commutative Banach algebras to topological algebras with a sequence of semi-norms (F-algebras).The question of what functions "operate" on an F-algebra is considered.It is proven that analytic functions in several complex variables operate by applying a theorem due to Waelbroeck.If all continuous functions operate on an F-algebra, then it is an algebra of continuous functions.However, unlike the situation for Banach algebras [6], it is not true that if V operates the algebra is C(Δ).This will be shown by an example.A theorem due to Curtis [4], concerning continuity of derivations when the algebra is regular is extended to F-algebras.The result is applied to an algebra of Lipschitz functions to show that it has only a trivial derivation.