A Class of Commutative Banach Algebras with Unique Complete Norm Topology and Continuous Derivations

John A. Lindberg
1971 Proceedings of the American Mathematical Society  
Let A be a semisimple commutative complex algebra with identity and a(x) a monic polynomial over A. Two results are is a Banach algebra under some norm, then B has a unique complete norm topology. Furthermore, B has nontrivial derivations if and only if B has a nontrivial radical.
doi:10.2307/2038589 fatcat:2ffdbyvwozem7ikxb2q7hd6ao4