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
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 $c_0$.References
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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: schlump@math.tamu.edu
- Vladimir G. Troitsky
- Affiliation: Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
- Email: vtroitsky@math.ualberta.ca
- 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: https://doi.org/10.1090/S0002-9939-02-06896-X
- MathSciNet review: 1949870