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ISSN 1088-6850(e) ISSN 0002-9947(p)

Hyperinvariant subspaces for some subnormal operators

Author(s): C. Foias; I. B. Jung; E. Ko; C. Pearcy
Journal: Trans. Amer. Math. Soc. 359 (2007), 2899-2913.
MSC (2000): Primary 47A15, 47B20
Posted: 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 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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