A note on transitive localizing algebras

Author:
Miguel Lacruz

Journal:
Proc. Amer. Math. Soc. **137** (2009), 3421-3423

MSC (2000):
Primary 47A15; Secondary 47L10

DOI:
https://doi.org/10.1090/S0002-9939-09-09924-9

Published electronically:
May 14, 2009

MathSciNet review:
2515411

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Abstract | References | Similar Articles | Additional Information

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

Email:
lacruz@us.es

DOI:
https://doi.org/10.1090/S0002-9939-09-09924-9

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.