Dales, H.G. and McClure, J. P. (1975) Completion of normed algebras of polunomials. Journal of the Australian Mathematical Society, 20 (4). pp. 504510. ISSN 14467887

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Abstract
Let P be the algebra of polynomials in one inderminate x over the complex field C. Suppose xs2225 · xs2225 is a norm on P such that the coefficient functionals cj: ∑αix1 → αj (j = 0,1,2,…) are all continuous with respect to xs2225·xs2225, and Let K xs2282 C be the set of characters on P which are xs2225·xs2225continuous. then K is compact, C\K is connected, and 0xs2208K. K. Let A be the completion of P with respect to xs2225·xs2225. Then A is a singly generated Banach algebra, with space of characters (homeomorphic with) K. The functionals cj have unique extensions to bounded linear functionals on A, and the map a →∑Ci(a)xi (a xs2208 A) is a homomorphism from A onto an algebra of formal power series with coefficients in C. We say that A is an algebra of power series if this homomorphism is onetoone, that is if a xs2208 A and a≠O imply cj(a)≠ 0 for some j.
Item Type:  Journal Article 

Journal or Publication Title:  Journal of the Australian Mathematical Society 
Additional Information:  http://journals.cambridge.org/action/displayJournal?jid=JAZ The final, definitive version of this article has been published in the Journal, Journal of the Australian Mathematical Society, 20 (4), pp 504510 1975, © 1975 Cambridge University Press. 
Uncontrolled Keywords:  /dk/atira/pure/subjectarea/asjc/2600 
Subjects:  
Departments:  Faculty of Science and Technology > Mathematics and Statistics 
ID Code:  67727 
Deposited By:  ep_importer_pure 
Deposited On:  26 Nov 2013 12:04 
Refereed?:  Yes 
Published?:  Published 
Last Modified:  29 Jan 2020 02:15 
URI:  https://eprints.lancs.ac.uk/id/eprint/67727 
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