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Invariant subspaces of super left-commutants


Author: Hailegebriel E. Gessesse
Journal: Proc. Amer. Math. Soc. 137 (2009), 1357-1361
MSC (2000): Primary 47A15; Secondary 46B42, 47B65
DOI: https://doi.org/10.1090/S0002-9939-08-09673-1
Published electronically: October 6, 2008
MathSciNet review: 2465659
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Abstract: For a positive operator $ Q$ on a Banach lattice, one defines $ \langle Q]=\{T\geq 0\,:\,~TQ\leq QT\}$ and $ [Q\rangle=\{T\geq 0\,:\, TQ\geq QT\}$. There have been several recent results asserting that, under certain assumptions on $ Q$, $ [Q\rangle$ has a common invariant subspace. In this paper, we use the technique of minimal vectors to establish similar results for $ \langle Q]$.


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Additional Information

Hailegebriel E. Gessesse
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G2G1, Canada
Email: hgessesse@math.ualberta.ca

DOI: https://doi.org/10.1090/S0002-9939-08-09673-1
Keywords: Invariant subspace, quasinilpotent operator, positive operator
Received by editor(s): April 11, 2008
Published electronically: October 6, 2008
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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