Hyperinvariant subspaces for some subnormal operators
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- by C. Foias, I. B. Jung, E. Ko and C. Pearcy PDF
- Trans. Amer. Math. Soc. 359 (2007), 2899-2913 Request permission
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.References
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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
- MR Author ID: 353576
- Email: eiko@ewha.ac.kr
- C. Pearcy
- Affiliation: Department of Mathematics, Texas A & M University, College Station, Texas 77843
- Email: pearcy@math.tamu.edu
- Received by editor(s): January 18, 2005
- Received by editor(s) in revised form: June 24, 2005
- Published electronically: January 4, 2007
- © Copyright 2007 American Mathematical Society
- 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
- MathSciNet review: 2286062