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 | References | Similar Articles | Additional Information

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 does not converge in the SOT to the identity operator or 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