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Banach Algebras Which are a Direct Sum of Division Algebras

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  09 April 2009

Antonio Fernandez Lopez  and
Eulalia Garcia Rus
Antonio Fernandez Lopez
Affiliation:
Departamento de Algebra, Geometria y Topologia Universidad de Malaga29080 Malaga, Spain
Eulalia Garcia Rus
Affiliation:
Departamento de Algebra, Geometria y Topologia Universidad de Malaga29080 Malaga, Spain
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Abstract

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In this note it is proved that a (real or complex) semiprime Banach algebra A satisfying xAx = x2Ax2 for every x ∈ A is a direct sum of a finite number of division Banach algebras.

Keywords

Banach algebrasemiprimedivision algebra

MSC classification

Secondary: 46H20: Structure, classification of topological algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 2 , April 1988 , pp. 143 - 145
Copyright
Copyright © Australian Mathematical Society 1988

References

Esterle, J. and Oudadess, M. (1986), ‘Structure of Banach algebras A satisfying Ax2 = Ax for every x ∈ A’, Proc. Amer. Math. Soc. (1) 96, 91–94.Google Scholar
Jacobson, N. (1956), Structure of rings, (Amer. Math. Soc. Colloq. Publ., Vol. 37, Amer. Math. Soc. Providence, R.I.).Google Scholar
Kaplansky, I. (1948), ‘Regular Banach algebras’, J. Indian Math. Soc. 12, 57–62.Google Scholar
Rickart, C. E. (1974), General theory of Banach algebras, (Krieger).Google Scholar