A remark on invariant subspaces of positive operators
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- by Vladimir G. Troitsky PDF
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Abstract:
If $S$, $T$, $R$, and $K$ are non-zero positive operators on a Banach lattice such that $S\leftrightarrow T\leftrightarrow R\leqslant K$, where “$\leftrightarrow$” stands for the commutation relation, $T$ is non-scalar, and $K$ is compact, then $S$ has an invariant subspace.References
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Additional Information
- Vladimir G. Troitsky
- Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6GÂ 2G1, Canada
- Email: troitsky@ualberta.ca
- 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
- © Copyright 2013 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 141 (2013), 4345-4348
- MSC (2010): Primary 47B65; Secondary 47A15
- DOI: https://doi.org/10.1090/S0002-9939-2013-11709-0
- MathSciNet review: 3105876