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Spring Topology and Dynamical Systems Conference 2008
March 13-15, 2008
University of Wisconsin Milwaukee and Marquette University
Milwaukee, WI, USA

Organizers
Ric Ancel, Karen Brucks, Craig Guilbault, Chris Hruska, Suzanne Hruska, Boris Okun (UWM); Paul Bankston (Marquette); Lois Kailhofer (Alverno College).

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Common hypercyclic and supercyclic vectors
by
Rebecca Sanders
Marquette University
Coauthors: Kit Chan (Bowling Green State University)

Given a Banach space X and a linear operator T on X, a vector x is a hypercyclic vector for T if its Orb(T, x) is dense in X. A vector x is a supercyclic vector for T if the set of all scalar multiples of vectors from the orbit Orb(T, x) is dense in X. We give necessary and sufficient conditions for a path of operators to have a dense Gd set of common hypercyclic vectors and common supercyclic vectors. We then apply this result to paths of unilateral weighted backward shift operators.

Date received: February 19, 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 # cawk-51.