Journal of Operator Theory

Volume 62, Issue 1, Summer 2009 pp. 65-81.

Common cyclic vectors for unitary operators

Authors: William T. Ross (1) and Warren R. Wogen (2)
Author institution: (1) Department of Mathematics and Computer Science, University of Richmond, Richmond, VI 23173, U.S.A.
(2) Department of Mathematics, University of North Carolina - Chapel Hill, Chapel Hill, NC 27599, U.S.A.

Summary: In this paper, we determine whether or not certain natural classes of unitary multiplication operators on $L^2(\mathrm d\theta)$ have common cyclic vectors. For some classes which have common cyclic vectors, we obtain a classification of these vectors.

Keywords: Unitary operators, multiplication operators, cyclic vectors, Szeg\"{o}'s theorem.

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