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Journal of Operator Theory

Volume 80, Issue 2,  Fall  2018  pp. 349-374.

Hypercyclic shift factorizations for unilateral weighted backward shift operators

Authors:  Kit C. Chan (1) and Rebecca Sanders (2)
Author institution: (1) Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, 43403, U.S.A.
(2) Department of Mathematics, Statistics, and Computer Science, Marquette University, Milwaukee, 53201, U.S.A.

Summary:  We show that every unilateral weighted backward shift $T$ on $\ell^p$, where $1\leqslant p < \infty$, has the factorization $T = AB$ with two hypercyclic operators $A$ and $B$, one of which is a unilateral weighted backward shift and the other one is a bilateral weighted shift.

Keywords:  weighted shift, hypercyclic operator, chaotic operator, factorization

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