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

 

Continuity of higher derivations


Author: R. J. Loy
Journal: Proc. Amer. Math. Soc. 37 (1973), 505-510
MSC: Primary 46H05
MathSciNet review: 0312265
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Abstract: Let A and B be two algebras over the complex field C. A sequence $ {\{ {F_n}\} _{0 \leqq n \leqq m}}$ (resp. $ {\{ {F_n}\} _{0 \leqq n < \infty }}$) of linear operators from A into B is a higher derivation of rank m (resp. infinite rank) if, for each $ n = 0,1, \cdots ,m$ (resp. $ n = 0,1, \cdots $) and any $ x,y \in A$,

$\displaystyle {F_n}(xy) = \sum\limits_{i = 0}^n {{F_i}(x){F_{n - i}}(y).} $

We consider the continuity of such $ \{ {F_n}\} $ when A and B are commutative topological algebras with complete metrizable topology. Some applications are given to algebras of formal power series.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0312265-9
PII: S 0002-9939(1973)0312265-9
Keywords: Higher derivations, continuity of derivations, complete metrizable topological algebra
Article copyright: © Copyright 1973 American Mathematical Society