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Commutators of compact operators

Anderson, Joel (1977) Commutators of compact operators. Journal für die reine und angewandte Mathematik, 1977 (291). pp. 128-132. ISSN 1435-5345. doi:10.1515/crll.1977.291.128.

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In [4] Pearcy and Topping initiated the study of additive commutators of compact operators on Hilbert space and asked if each projection of rank one has this form. In [3] Brown and Schochet raised a more general question. Suppose H is an algebra of operators that contains the trace class operators and is commutative modulo the trace class operators. If A and B are elements of H and A is compact, then does the commutator [A,B] = AB – BA have trace 0? (This question arose from an attempt to generalize certain results obtained by Brown [2], Section 3, in the case where H is also a *-algebra.

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Additional Information:© 1977 by Walter de Gruyter GmbH.
Issue or Number:291
Record Number:CaltechAUTHORS:20180806-135101571
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:88613
Deposited By: Tony Diaz
Deposited On:06 Aug 2018 21:05
Last Modified:16 Nov 2021 00:28

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