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A note on transitive localizing algebras

Author: Miguel Lacruz
Journal: Proc. Amer. Math. Soc. 137 (2009), 3421-3423
MSC (2000): Primary 47A15; Secondary 47L10
Published electronically: May 14, 2009
MathSciNet review: 2515411
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Abstract: A simple proof is provided for a theorem of Troitsky that every nonzero quasinilpotent operator on a Banach space whose commutant is a localizing algebra has a nontrivial hyperinvariant subspace.

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Additional Information

Miguel Lacruz
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Avenida Reina Mercedes s/n, 41012 Sevilla, Spain

Keywords: Invariant subspace, localizing algebra, quasinilpotent operator
Received by editor(s): August 7, 2008
Received by editor(s) in revised form: December 31, 2008, and February 13, 2009
Published electronically: May 14, 2009
Additional Notes: This research was partially supported by Junta de Andalucía under Grant FQM-3737.
Communicated by: Marius Junge
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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