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


Joins and intersections of ideals of compact operators

Author: Allen Schweinsberg
Journal: Proc. Amer. Math. Soc. 59 (1976), 268-272
MSC: Primary 46L15; Secondary 47B10
MathSciNet review: 0454670
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Abstract: It is shown that certain well-known ideals of compact operators are the intersection of a decreasing, countable family of strictly larger ideals. Also, it is shown that if $ {T_1}$ and $ {T_2}$ are compact operators, neither of which lies in the principal ideal generated by the other, and if $ \mathcal{I}$ is an arbitrary countably generated ideal, then there exist ideals $ {\mathcal{J}_1}$ and $ {\mathcal{J}_2}$ such that $ \mathcal{I} \subseteq {\mathcal{J}_1} \vee {\mathcal{J}_2}$ and $ {T_i} \notin {\mathcal{J}_i},\;i = 1,\,2$.

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PII: S 0002-9939(1976)0454670-9
Article copyright: © Copyright 1976 American Mathematical Society