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On Fréchet algebras of power series

Published online by Cambridge University Press:  17 April 2009

S. J. Bhatt  and
S. R. Patel
S. J. Bhatt
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388 120, Gujarat, India e-mail: sjb@spu.ernet.in, coolpatel1@yahoo.com
S. R. Patel
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388 120, Gujarat, India e-mail: sjb@spu.ernet.in, coolpatel1@yahoo.com
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Abstract

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If the indeterminate X in a Fréchet 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-Fréchet 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 Fréchet 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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 1 , August 2002 , pp. 135 - 148
Copyright
Copyright © Australian Mathematical Society 2002

References

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