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

DOI:
https://doi.org/10.1090/S0002-9947-1978-0515547-X

MathSciNet review:
515547

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the ring of bounded operators on a separable Hubert space. Assuming the continuum hypothesis, we prove that in 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 . 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:
https://doi.org/10.1090/S0002-9947-1978-0515547-X

Keywords:
Hubert space,
operator ideals,
compact operators,
continuum hypothesis,
axiom of choice,
Calkin ideal sets

Article copyright:
© Copyright 1978
American Mathematical Society