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A Class of Invertible Bilateral Weighted Shifts
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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.
Abstract
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.
참고문헌 (6)
- A. Atzmon, "On the existence of hyperinvariant subspaces", J. Operator Theory, 11, pp.3~40 (1984)
- L. A. Fialkow, "A note on quasisimilarility of operators", Acta Sci. Math, 39, pp.67~85 (1977)
- H. Radjavi, "Invariant subspaces" (2002), Dover Publ. Inc
- H. Rosenthal, "A weighted bilateral shift which is a possible counter-example to the hyperinvariant subspace problem"
- H. Rosenthal, "A new direction in classical harmonic analysis with applications to the hyperinvariant subspace problem"
- A. Shields, "Weighted shift operators and analytic function theory", pp.49~128 (1974), Amer. Math. Soc.
관련 논문AI추천
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