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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

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


Author: John A. Lindberg
Journal: Proc. Amer. Math. Soc. 29 (1971), 516-520
MSC: Primary 46.55
MathSciNet review: 0278076
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0278076-6
PII: S 0002-9939(1971)0278076-6
Keywords: Uniqueness of complete norm topology, continuous derivations, normed extensions, commutative Banach algebras
Article copyright: © Copyright 1971 American Mathematical Society