Operators with bounded conjugation orbits
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- by D. Drissi and M. Mbekhta PDF
- Proc. Amer. Math. Soc. 128 (2000), 2687-2691 Request permission
Abstract:
For a bounded invertible operator $A$ on a complex Banach space $X,$ let $B_A$ be the set of operators $T$ in $\mathcal {L} (X)$ for which $\sup _{n \geq 0} \|A^n T A^{-n}\| < \infty .$ Suppose that $Sp(A) = \{1\}$ and $T$ is in $B_A \cap B_{A^{-1}}.$ A bound is given on $\|ATA^{-1} - T\|$ in terms of the spectral radius of the commutator. Replacing the condition $T$ in $B_{A^{-1}}$ by the weaker condition $\|A^{-n} T A^n\| = o(e^{\epsilon \sqrt {n}}),$ as $n \to \infty$ for every $\epsilon >0$, an extension of the Deddens-Stampfli-Williams results on the commutant of $A$ is given.References
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Additional Information
- D. Drissi
- Affiliation: Department of Mathematics and Computer Science, Faculty of Science, Kuwait University, P. O. Box 5969, Safat 13060, Kuwait
- Email: drissi@math-1.sci.kuniv.edu.kw
- M. Mbekhta
- Affiliation: URA 751 au CNRS & UFR de Mathematiques, Université de Lille I, F-59655, Villeneuve d’asq, France; Université de Galatasaray, Ciragan Cad no. 102, Ortakoy 80840, Istanbul, Turquie
- MR Author ID: 121980
- Email: Mostafa.Mbekhta@univ-lille1.fr
- Received by editor(s): June 23, 1998
- Received by editor(s) in revised form: October 27, 1998
- Published electronically: April 27, 2000
- Additional Notes: The first author acknowledges support from Kuwait University
- Communicated by: David R. Larson
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2687-2691
- MSC (1991): Primary 47B10, 47B15
- DOI: https://doi.org/10.1090/S0002-9939-00-05338-7
- MathSciNet review: 1664345