Hyperinvariant subspaces for some subnormal operators

Foias, C.; Jung, I.; Ko, E.; Pearcy, C.

doi:10.1090/S0002-9947-07-04113-X

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.

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