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19th International Conference on Operator Theory
June 27 - July 2, 2002
Institute of Mathematics of the Romanian Academy and the Faculty of Mathematics of the West University of Timisoara
Timisoara, Romania

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Power bounded operators and supercyclic vectors
by
Vladimir Muller
Mathematical Institute, Czech Academy of Sciences

By the well-known result of Brown, Chevreau and Pearcy, each Hilbert space contraction with spectrum containing the unit circle has a nontrivial closed invariant subspace. Equivalently, there is a nonzero vector which is not cyclic. We show that each Hilbert space contraction (or more generally, power bounded operator) whose spectrum contains at least one point from the unit circle has a nonzero vector which is not supercyclic. Equivalently, there is a nontrivial closed invariant homogeneous subset.

Date received: June 10, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caiz-58.