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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 boundedness, invariant subspaces and similarity to contractions
by
Gilles Cassier
Institut Girard Desargues, UMR 5028 au CNRS, université Claude Bernard Lyon 1, France.

In the first part of the talk, we make a thorough investigation concerning the behaviour of an operator T on an invariant subspace E and on the orthogonal complement of E with the possibility for T to be similar to a contraction [1]. The aim of the second part, which comes from a joint work with Dan Timotin [2], is to explore the applications of the results of [1] to a distinguished particulary case, namely one dimensional perturbations of the shift operator.

[1] Gilles Cassier, Generalized Toeplitz operators, restrictions to invariant subspaces and similarity problems, preprint.

[2] Gilles Cassier and Dan Timotin, Power boundedness and similarity to contractions for some perturbations of isometries, preprint.

Date received: June 15, 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-74.