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Proceedings of the American Mathematical Society

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A note on multiplicatively prime ideals of operators


Author: Pei-Kee Lin
Journal: Proc. Amer. Math. Soc. 101 (1987), 462-464
MSC: Primary 47D25
DOI: https://doi.org/10.1090/S0002-9939-1987-0908649-8
MathSciNet review: 908649
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Abstract: An ideal $ \mathcal{I}$ of $ \mathcal{L}(\mathcal{H})$ is said to be multiplicatively prime if $ AXB \in \mathcal{I}$ for all $ X \in \mathcal{L}(\mathcal{H})$ implies $ A$ or $ B$ is in $ \mathcal{I}$. In this paper, we show there exists a nonnorm multiplicatively prime ideal other than $ \mathcal{F}$.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0908649-8
Article copyright: © Copyright 1987 American Mathematical Society