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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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