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Operators that are not orbit-reflexive
by
Jan Vrsovsky
Institute of Mathematics, Prague
Coauthors: Vladimir Muller
A bounded linear operator T is called orbit-reflexive if the following equivalence holds: an operator A belongs to the closure of the powers of T in the strong operator topology iff for any point x, Ax belongs to the closure of the orbit of x under T.
We sketch two recent constructions of operators that are not orbit-reflexive. The first is a Read-type construction in Hilbert space, due to Grivaux and Roginskaya, and the second can be described as a binding of several weighted shifts, providing a reflexive Banach space example.
Date received: June 18, 2008
Copyright © 2008 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 # caxn-27.