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    Rights statement: 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 504-510 1975, © 1975 Cambridge University Press.

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Completion of normed algebras of polunomials

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Completion of normed algebras of polunomials. / Dales, H.G.; McClure, J. P.

In: Journal of the Australian Mathematical Society, Vol. 20, No. 4, 11.1975, p. 504-510.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Dales, HG & McClure, JP 1975, 'Completion of normed algebras of polunomials', Journal of the Australian Mathematical Society, vol. 20, no. 4, pp. 504-510. https://doi.org/10.1017/S1446788700016207

APA

Dales, H. G., & McClure, J. P. (1975). Completion of normed algebras of polunomials. Journal of the Australian Mathematical Society, 20(4), 504-510. https://doi.org/10.1017/S1446788700016207

Vancouver

Dales HG, McClure JP. Completion of normed algebras of polunomials. Journal of the Australian Mathematical Society. 1975 Nov;20(4):504-510. https://doi.org/10.1017/S1446788700016207

Author

Dales, H.G. ; McClure, J. P. / Completion of normed algebras of polunomials. In: Journal of the Australian Mathematical Society. 1975 ; Vol. 20, No. 4. pp. 504-510.

Bibtex

@article{e4feb32ddae340ebb96531f8db6c11f9,
title = "Completion of normed algebras of polunomials",
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·xs2225-continuous. 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 one-to-one, that is if a xs2208 A and a≠O imply cj(a)≠ 0 for some j.",
author = "H.G. Dales and McClure, {J. P.}",
note = "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 504-510 1975, {\textcopyright} 1975 Cambridge University Press.",
year = "1975",
month = nov,
doi = "10.1017/S1446788700016207",
language = "English",
volume = "20",
pages = "504--510",
journal = "Journal of the Australian Mathematical Society",
issn = "1446-7887",
publisher = "Cambridge University Press",
number = "4",

}

RIS

TY - JOUR

T1 - Completion of normed algebras of polunomials

AU - Dales, H.G.

AU - McClure, J. P.

N1 - 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 504-510 1975, © 1975 Cambridge University Press.

PY - 1975/11

Y1 - 1975/11

N2 - 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·xs2225-continuous. 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 one-to-one, that is if a xs2208 A and a≠O imply cj(a)≠ 0 for some j.

AB - 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·xs2225-continuous. 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 one-to-one, that is if a xs2208 A and a≠O imply cj(a)≠ 0 for some j.

U2 - 10.1017/S1446788700016207

DO - 10.1017/S1446788700016207

M3 - Journal article

VL - 20

SP - 504

EP - 510

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

SN - 1446-7887

IS - 4

ER -