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

 

A remark on invariant subspaces of positive operators


Author: Vladimir G. Troitsky
Journal: Proc. Amer. Math. Soc. 141 (2013), 4345-4348
MSC (2010): Primary 47B65; Secondary 47A15
Published electronically: August 28, 2013
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Abstract: If $ S$, $ T$, $ R$, and $ K$ are non-zero positive operators on a Banach lattice such that $ S\leftrightarrow T\leftrightarrow R\le K$, where `` $ \leftrightarrow $'' stands for the commutation relation, $ T$ is non-scalar, and $ K$ is compact, then $ S$ has an invariant subspace.


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Additional Information

Vladimir G. Troitsky
Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G2G1, Canada
Email: troitsky@ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11709-0
PII: S 0002-9939(2013)11709-0
Keywords: Positive operators, invariant subspaces
Received by editor(s): December 1, 2011
Received by editor(s) in revised form: February 8, 2012, and February 19, 2012
Published electronically: August 28, 2013
Additional Notes: The author was supported by NSERC
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2013 American Mathematical Society