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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 | References | Similar Articles | Additional Information

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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  • 1. N. Bourbaki, Éléments de Mathématique, Groupes et Algébres de Lie, Hermann, Paris, 1971 (chapitres 1-3). MR 0271276 (42:6159)
  • 2. N. Jacobson, Lie Algebras, Interscience, New York, 1962. MR 0143793 (26:1345)
  • 3. H. Radjavi, P. Rosenthal, Simultaneous Triangularization, Universitext, Springer-Verlag, New York, 2000. MR 1736065 (2001e:47001)
  • 4. C.J. Read, Quasinilpotent Operators and the Invariant Subspace Problem, J. London Math. Soc. (2) 56 (1997), no. 3, 595-606. MR 1610408 (98m:47004)
  • 5. F. Riesz, B. Sz.-Nagy, Leçons d'Analyse Fonctionnelle, Akadémiai Kiadó, Budapest, 1952. MR 0050159 (14:286d), MR 0179567 (31:3815)
  • 6. J.R. Ringrose, Compact Non-Self-Adjoint Operators, Van Nostrand, London, 1971.
  • 7. V. Shulman, Y. Turovskiı, Joint Spectral Radius, Operator Semigroups, and a Problem of W. Wojtynski, J. Funct. Anal. 177 (2000), no. 2, 383-441. MR 1795957 (2002d:47099)
  • 8. V. Shulman, Y. Turovskiı, Invariant Subspaces of Operator Lie Algebras and Lie Algebras with Compact Adjoint Action, J. Funct. Anal. 223 (2005), no. 2, 425-508. MR 2142346 (2006a:47098)
  • 9. W. Wojtyński, Engel's Theorem for Nilpotent Lie Algebras of Hilbert-Schmidt Operators, Bull. Acad. Polon. Sci. 24 (9) (1976), 797-801. MR 0430808 (55:3813)
  • 10. W. Wojtyński, Banach-Lie Algebras of Compact Operators, Studia Math. 59 (1976/77), no. 3, 263-273. MR 0430806 (55:3811)

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Additional Information

Matthew Kennedy
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

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.

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