The strong radical and finite-dimensional ideals
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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.References
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Additional Information
- Bertram Yood
- Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
- Received by editor(s): January 7, 2000
- Received by editor(s) in revised form: June 10, 2000
- Published electronically: May 23, 2001
- Communicated by: Dale Alspach
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 139-143
- MSC (2000): Primary 46H10; Secondary 16D25
- DOI: https://doi.org/10.1090/S0002-9939-01-06049-X
- MathSciNet review: 1855630