A class of commutative Banach algebras with unique complete norm topology and continuous derivations

Lindberg, John A.

doi:10.1090/S0002-9939-1971-0278076-6

A class of commutative Banach algebras with unique complete norm topology and continuous derivations
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Proc. Amer. Math. Soc. 29 (1971), 516-520 Request permission

Abstract:

Let A be a semisimple commutative complex algebra with identity and $\alpha (x)$ a monic polynomial over A. Two results are proved. If $B = A[x]/(\alpha (x))$ 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.

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