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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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On quasi-affine transforms of Read’s operator
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by Thomas Schlumprecht and Vladimir G. Troitsky PDF
Proc. Amer. Math. Soc. 131 (2003), 1405-1413 Request permission


We show that C. J. Read’s example of an operator $T$ on $\ell _1$ which does not have any non-trivial invariant subspaces is not the adjoint of an operator on a predual of $\ell _1$. Furthermore, we present a bounded diagonal operator $D$ such that even though $D^{-1}$ is unbounded, the operator $D^{-1}TD$ is a bounded operator on $\ell _1$ with invariant subspaces, and is adjoint to an operator on $c_0$.
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Additional Information
  • Thomas Schlumprecht
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
  • MR Author ID: 260001
  • Email:
  • Vladimir G. Troitsky
  • Affiliation: Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
  • Email:
  • Received by editor(s): November 30, 2001
  • Published electronically: December 6, 2002
  • Additional Notes: The first author was supported by the NSF. Most of the work on the paper was done during the Workshop on linear analysis and probability at Texas A&M University, College Station
  • Communicated by: David R. Larson
  • © Copyright 2002 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 131 (2003), 1405-1413
  • MSC (2000): Primary 47A15; Secondary 47B37
  • DOI:
  • MathSciNet review: 1949870