Joins and intersections of ideals of compact operators
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- by Allen Schweinsberg PDF
- Proc. Amer. Math. Soc. 59 (1976), 268-272 Request permission
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
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Additional Information
- © Copyright 1976 American Mathematical Society
- 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