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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46.55

Retrieve articles in all journals with MSC: 46.55


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0278076-6
Keywords: Uniqueness of complete norm topology, continuous derivations, normed extensions, commutative Banach algebras
Article copyright: © Copyright 1971 American Mathematical Society