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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A remark on invariant subspaces of positive operators
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by Vladimir G. Troitsky PDF
Proc. Amer. Math. Soc. 141 (2013), 4345-4348 Request permission

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, T6G 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