The strong radical and finite-dimensional ideals

Yood, Bertram

doi:10.1090/S0002-9939-01-06049-X

The strong radical and finite-dimensional ideals
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Proc. Amer. Math. Soc. 130 (2002), 139-143 Request permission

Abstract:

Let $A$ be a semi-prime Banach algebra with strong radical ${\mathfrak R}$ (intersection of its two-sided modular maximal ideals). A minimal left or right ideal $K$ of $A$ is infinite-dimensional if and only if $K \subset {\mathfrak R}$. Thus all minimal one-sided ideals in $A$ are finite-dimensional if $A$ is strongly semi-simple.

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