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Continuity of derivations on topological algebras of power series

Published online by Cambridge University Press:  17 April 2009

R.J. Loy
R.J. Loy
Affiliation:
Department of Mathematics, Carleton University, Ottawa, Canada.
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Abstract

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Let A be an algebra of formal power series in one indeterminate over the complex field, D a derivation on A. It is shown that if A has a Fréchet space topology under which it is a topological algebra, then D is necessarily continuous provided the coordinate projections satisfy a certain equicontinuity condition. This condition is always satisfied if A is a Banach algebra and the projections are continuous. A second result is given, with weaker hypothesis on the projections and correspondingly weaker conclusion.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 3 , December 1969 , pp. 419 - 424
Copyright
Copyright © Australian Mathematical Society 1969

References

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