The Arens-Calderon theorem for commutative topological algebras.

A theorem of Arens and Calderon states that if A is a commutative Banach algebra with Jacobson radical Rad(A), and if a₀,..., a_n ∈ A with a₀ 2 Rad(A) and a₁ an invertible element of A, then there exists y ∈ Rad(A) such that ... n this paper, we give extensions of this result to commutative non-normed topological algebras, as this is vital for extending an embedding theorem of Allan in [2] regarding the embedding of the formal power series algebra C[[X]] into a commutative Banach algebra. [ABSTRACT FROM AUTHOR]