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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on ideals of operators


Author: Richard I. Loebl
Journal: Proc. Amer. Math. Soc. 96 (1986), 62-64
MSC: Primary 47D25
MathSciNet review: 813810
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Abstract: An ideal $ I$ of $ L\left( H \right)$ is said to be multiplicatively prime if $ AXB \in I$ for all $ X \in L\left( H \right)$ implies $ A$ or $ B$ is in $ I$. The only normable multiplicatively prime ideals are 0 and $ K$, the compacts. Multiplicative primeness is related to other properties an ideal may possess.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0813810-6
PII: S 0002-9939(1986)0813810-6
Article copyright: © Copyright 1986 American Mathematical Society