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Algebraic ideals of semiprime Banach algebras
Published online by Cambridge University Press: 18 May 2009
Abstract
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 <+∞.
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- Copyright © Glasgow Mathematical Journal Trust 1991
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