- S1446788700016207a
**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.Final published version, 299 KB, PDF document

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

Research output: Contribution to journal › Journal article › peer-review

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

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

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

@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",

}

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 -