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A Class of Invertible Bilateral Weighted Shifts
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  • Journal title : Kyungpook mathematical journal
  • Volume 53, Issue 2,  2013, pp.185-189
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2013.53.2.185
 Title & Authors
A Class of Invertible Bilateral Weighted Shifts
Jung, Il Bong; Pearcy, Carl;
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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.
bilateral shift;Rosenthal shift;hyperinvariant subspace;
 Cited by
A. Atzmon, On the existence of hyperinvariant subspaces, J. Operator Theory 11(1984), 3-40.

L. A. Fialkow, A note on quasisimilarility of operators, Acta Sci. Math. (Szeged) 39(1977), 67-85.

H. Radjavi and P. Rosenthal, Invariant subspaces, Dover Publ. Inc. 2nd ed., 2002.

H. Rosenthal, A weighted bilateral shift which is a possible counter-example to the hyperinvariant subspace problem, in preperation.

H. Rosenthal, A new direction in classical harmonic analysis with applications to the hyperinvariant subspace problem, preprint.

A. Shields, Weighted shift operators and analytic function theory, Topics Oper. Th., pp. 49-128. Math. Surveys, No. 13, Amer. Math. Soc., Providence, R. I., 1974.