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.
DOI: http://dx.doi.org/10.7900/jot.2017oct02.2198
Keywords: weighted shift, hypercyclic operator, chaotic operator,
factorization
Contents
Full-Text PDF