Journal of Operator Theory

Volume 47, Issue 2, Spring 2002 pp. 379-387.

Solution of a problem of Peller concerning similarity

Authors: N.J. Kalton (1), and C. Le Merdy (2)
Author institution: (1) Department of Mathematics, University of Missouri-Columbia, Columbia, MO 65211, USA
(2) Equipe de Mathematiques -- UMR 6623, Universite de Franche-Comte, F-25030 Besancon cedex, France

Summary: We answer a question of Peller by showing that for any $c>1$ there exists a power-bounded operator $T$ on a Hilbert space with the property that any operator $S$ similar to $T$ satisfies $\sup\limits_n\|S^n\|>c$.

Keywords: Power bounded operators, similarities, multipliers, weights

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