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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 result concerning derivations in Banach algebras


Author: J. Vukman
Journal: Proc. Amer. Math. Soc. 116 (1992), 971-975
MSC: Primary 46H05; Secondary 16W25, 46L57
MathSciNet review: 1079710
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Abstract: The main result: Let $ A$ be a Banach algebra over the complex field $ C$. Suppose there exists a continuous derivation $ D:A \to A$, such that $ \alpha {D^3} + {D^2}$ is a derivation for some $ \alpha \in C$. In this case $ D$ maps $ A$ into its radical.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1079710-7
PII: S 0002-9939(1992)1079710-7
Keywords: Banach algebra, commutative Banach algebra, $ {C^ * }$-algebra, prime ring, semiprime ring, derivation, inner derivation
Article copyright: © Copyright 1992 American Mathematical Society