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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Triangularization of a Jordan algebra of Schatten operators


Author: Matthew Kennedy
Journal: Proc. Amer. Math. Soc. 136 (2008), 2521-2527
MSC (2000): Primary 47A15; Secondary 17C65
Published electronically: February 7, 2008
MathSciNet review: 2390522
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Abstract: We show that a Jordan algebra of compact quasinilpotent operators which contains a nonzero trace class operator has a common invariant subspace. As a consequence of this result, we obtain that a Jordan algebra of quasinilpotent Schatten operators is simultaneously triangularizable.


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Additional Information

Matthew Kennedy
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Email: m3kennedy@uwaterloo.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09295-2
PII: S 0002-9939(08)09295-2
Received by editor(s): February 15, 2007
Received by editor(s) in revised form: April 16, 2007
Published electronically: February 7, 2008
Additional Notes: This research was supported by NSERC
Communicated by: Marius Junge
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.