Hostname: page-component-848d4c4894-pftt2 Total loading time: 0 Render date: 2024-06-05T10:17:51.119Z Has data issue: false hasContentIssue false
  • English
  • Français

A theorem in Banach algebras and its applications

Published online by Cambridge University Press:  17 April 2009

V.K. Srinivasan  and
Hu Shaing
V.K. Srinivasan
Affiliation:
Department of Mathematics, University of Texas at El Paso, El Paso, Texas, USA.
Hu Shaing
Affiliation:
Department of Mathematics, University of Texas at El Paso, El Paso, Texas, USA.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

If A is a complex Banach algebra which is also a Bezout domain, it is shown that for any prime p and a non-negative integer n, pn is not a topological divisor of zero. Using the above result it is shown that a complex Banach algebra which is a principal ideal domain is isomorphic to the complex field.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 20 , Issue 2 , April 1979 , pp. 247 - 252
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Berg, Lothar, Introduction to the operational calculus (North-Holland Series on Applied Mathematics and Mechanics, 2. North-Holland, Amsterdam, 1967).Google Scholar
[2]Hungerford, Thomas W., Algebra (Holt, Reinhart and Winston, New York; Montreal, Quebec; London; 1974).Google Scholar
[3]Shaing, Hu, “On some Gelfand-Mazur like theorems in topological algebras” (MSc thesis, University of Texas, El Paso, 1979).Google Scholar
[4]Larsen, R., Banach algebras, an introduction (Pure and Applied Mathematics, 24. Marcel Dekker, New York, 1973).Google Scholar
[5]Naimark, M.A., Normed algebras (translated from the second Russian edition by Boron, Leo F.. Wolters-Noordhoff, Groningen, 1972).Google Scholar
[6]Rickart, Charles E., General theory of Banach algebras (Van Nostrand, Princeton, New Jersey; Toronto; London; New York; 1960).Google Scholar
[7]Srinivasan, V.K., “On some Gelfand-Mazur like theorems in Banach algebras”, Bull. Austral. Math. Soc. 20 (1979), 211–215.CrossRefGoogle Scholar