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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
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 ${T_i} \notin {\mathcal {J}_i},\;i = 1, 2$.


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Article copyright: © Copyright 1976 American Mathematical Society