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On quasi-affine transforms of Read's operator

Authors: Thomas Schlumprecht and Vladimir G. Troitsky
Journal: Proc. Amer. Math. Soc. 131 (2003), 1405-1413
MSC (2000): Primary 47A15; Secondary 47B37
Published electronically: December 6, 2002
MathSciNet review: 1949870
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Abstract: 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

Vladimir G. Troitsky
Affiliation: Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

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
Article copyright: © Copyright 2002 American Mathematical Society