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Algebraic ideals of semiprime Banach algebras

Published online by Cambridge University Press:  18 May 2009

S. Giotopoulos  and
M. Roumeliotis
S. Giotopoulos
Affiliation:
Department of Mathematics, Athens University, Panepistemiopolis, 15784 Athens, Greece
M. Roumeliotis
Affiliation:
Department of Mathematics, Athens University, Panepistemiopolis, 15784 Athens, Greece
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Abstract

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If A is a semiprime Banach algebra, soc A, rad A the socle and radical of A, then Soc A ∩ rad A = (0). This elementary result enables us to prove some results concerning algebraic ideal and algebraic elements modulo the socle of A. We also deduce several conditions for A equivalent to the condition dim A <+∞.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 3 , September 1991 , pp. 359 - 363
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

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