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Continuity of derivations on topological algebras of power series
Published online by Cambridge University Press: 17 April 2009
Abstract
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
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