Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47D25, 03E50

Retrieve articles in all journals with MSC: 47D25, 03E50

Additional Information

Keywords: Hubert space, operator ideals, compact operators, continuum hypothesis, axiom of choice, Calkin ideal sets
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society