Hyperinvariant subspaces for some subnormal operators

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

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

Hyperinvariant subspaces for some subnormal operators

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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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^*nSⁿ)^1/n} does not converge in the SOT to the identity operator or {(SⁿS ^*n)^1/n} does not converge in the SOT to zero has a nontrivial hyperinvariant subspace.

Original language	English
Pages (from-to)	2899-2913
Number of pages	15
Journal	Transactions of the American Mathematical Society
Volume	359
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9947-07-04113-X
State	Published - Jun 2007

Keywords

Hyperinvariant subspaces
Spectral measures
Subnormal operators

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10.1090/S0002-9947-07-04113-X

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AU - Ko, E.

AU - Pearcy, C.

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N2 - 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*nSn)1/n} does not converge in the SOT to the identity operator or {(SnS *n)1/n} does not converge in the SOT to zero has a nontrivial hyperinvariant subspace.

AB - 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*nSn)1/n} does not converge in the SOT to the identity operator or {(SnS *n)1/n} does not converge in the SOT to zero has a nontrivial hyperinvariant subspace.

KW - Hyperinvariant subspaces

KW - Spectral measures

KW - Subnormal operators

UR - https://www.scopus.com/pages/publications/77950987992

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JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

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ER -

Hyperinvariant subspaces for some subnormal operators

Abstract

Keywords

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