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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A characterization and sum decomposition for operator ideals


Authors: Andreas Blass and Gary Weiss
Journal: Trans. Amer. Math. Soc. 246 (1978), 407-417
MSC: Primary 47D25; Secondary 03E50
MathSciNet review: 515547
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Abstract: Let $ L(H)$ be the ring of bounded operators on a separable Hubert space. Assuming the continuum hypothesis, we prove that in $ L(H)$ every two-sided ideal that contains an operator of infinite rank is the sum of two smaller two-sided ideals. The proof involves a new combinatorial description of ideals of $ L(H)$. This description is also used to deduce some related results about decompositions of ideals. Finally, we discuss the possibility of proving our main theorem under weaker assumptions than the continuum hypothesis and the impossibility of proving it without the axiom of choice.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0515547-X
PII: S 0002-9947(1978)0515547-X
Keywords: Hubert space, operator ideals, compact operators, continuum hypothesis, axiom of choice, Calkin ideal sets
Article copyright: © Copyright 1978 American Mathematical Society