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Proceedings of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9939-1976-0454670-9
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$.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/S0002-9939-1976-0454670-9
Article copyright: © Copyright 1976 American Mathematical Society

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