Corrigendum Et Addendum A L'Article "Unite Et Semi-Normes Dans Les Algebres Localement Convexes".
We consider topological algebras in which all left ideals are closed. We show, in particular, that an F-algebra has this property if, and only if, it is a noetherian Q-algebra.
We prove that C*-algebras for an equivalent norm are the involutive Banach algebras which admit the continuous functional calculus.
We show that the Banach algebras with continuous involution are the Banach algebras which admit a harmonic functional calculus, while we prove that the hermitian commutative Banach algebras are exactly the involutive commutative Banach algebras that admit a real analytic functional calculus.
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