Bhatta, S. J. ; Patel, S. R. (2002) On Frèchet algebras of power series Bulletin of the Australian Mathematical Society, 66 (01). pp. 135148. ISSN 00049727

PDF
 Publisher Version
573kB 
Official URL: http://journals.cambridge.org/action/displayAbstra...
Related URL: http://dx.doi.org/10.1017/S000497270002075X
Abstract
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 BeurlingFrèchet algebra on nonnegative 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 nonBanach 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.
Item Type:  Article 

Source:  Copyright of this article belongs to Australian Mathematical Society. 
ID Code:  59672 
Deposited On:  07 Sep 2011 05:18 
Last Modified:  18 May 2016 10:09 
Repository Staff Only: item control page