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Hyperinvariant subspaces for some subnormal operators


Authors: C. Foias, I. B. Jung, E. Ko and C. Pearcy
Journal: Trans. Amer. Math. Soc. 359 (2007), 2899-2913
MSC (2000): Primary 47A15, 47B20
DOI: https://doi.org/10.1090/S0002-9947-07-04113-X
Published electronically: January 4, 2007
MathSciNet review: 2286062
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Abstract: In this article we employ a technique originated by Enflo in 1998 and later modified by the authors to study the hyperinvariant subspace problem for subnormal operators. We show that every ``normalized''subnormal operator $ S$ such that either $ \{(S^{\ast n}S^{n})^{1/n}\}$ does not converge in the SOT to the identity operator or $ \{(S^{n}S^{\ast n})^{1/n}\}$ does not converge in the SOT to zero has a nontrivial hyperinvariant subspace.


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Additional Information

C. Foias
Affiliation: Department of Mathematics, Texas A & M Univeristy, College Station, Texas 77843
Email: foias@math.tamu.edu

I. B. Jung
Affiliation: Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 701-701, Korea
Email: ibjung@mail.knu.ac.kr

E. Ko
Affiliation: Department of Mathematics, Ewha Women’s University, Seoul 120-750, Korea
Email: eiko@ewha.ac.kr

C. Pearcy
Affiliation: Department of Mathematics, Texas A & M University, College Station, Texas 77843
Email: pearcy@math.tamu.edu

DOI: https://doi.org/10.1090/S0002-9947-07-04113-X
Keywords: Subnormal operators, hyperinvariant subspaces, spectral measures.
Received by editor(s): January 18, 2005
Received by editor(s) in revised form: June 24, 2005
Published electronically: January 4, 2007
Article copyright: © Copyright 2007 American Mathematical Society

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