On Frèchet algebras of power series

Bhatta, S. J. ; Patel, S. R. (2002) On Frèchet algebras of power series Bulletin of the Australian Mathematical Society, 66 (01). pp. 135-148. ISSN 0004-9727

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Related URL: http://dx.doi.org/10.1017/S000497270002075X


If the indeterminate X in a Frèchet algebra A of power series is a power series generator for A, then either A is the algebra of all formal power series or is the Beurling-Frèchet algebra on non-negative integers defined by a sequence of weights. Let the topology of A be defined by a sequence of norms. Then A is an inverse limit of a sequence of Banach algebras of power series if and only if each norm in the defining sequence satisfies certain closability condition and an equicontinuity condition due to Loy. A non-Banach uniform Frèchet algebra with a power series generator is a nuclear space. A number of examples are discussed; and a functional analytic description of the holomorphic function algebra on a simply connected planar domain is obtained.

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Source:Copyright of this article belongs to Australian Mathematical Society.
ID Code:59672
Deposited On:07 Sep 2011 05:18
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