Original Article
Kyungpook Mathematical Journal 2013; 53(2): 185-189
Published online June 23, 2013
Copyright © Kyungpook Mathematical Journal.
A Class of Invertible Bilateral Weighted Shifts
Il Bong Jung1 , Carl Pearcy2
1 Department of Mathematics, Kyungpook National University, Daegu, 702-701, Korea
2 Department of Mathematics, Texas A&M University, College Station, TX 77843, USA
In this note we study a class of invertible weighted bilateral shifts on Hilbert space introduced by Haskell Rosenthal recently. We show that every Rosenthal shift is unitarily equivalent to its inverse, not quasisimilar to its adjoint, and has a nontrivial hyperinvariant subspace.
Keywords: bilateral shift, Rosenthal shift, hyperinvariant subspace