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