Spectral decomposability of rank-one perturbations of normal operators

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

doi:10.1016/j.jmaa.2010.09.037

Spectral decomposability of rank-one perturbations of normal operators

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

Department of Mathematics

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

16 Scopus citations

Abstract

This paper is a continuation of the study by Foias, Jung, Ko, and Pearcy (2007) [4] and Foias, Jung, Ko, and Pearcy (2008) [5] of rank-one perturbations of diagonalizable normal operators. In Foias, Jung, Ko, and Pearcy (2007) [4] we showed that there is a large class of such operators each of which has a nontrivial hyperinvariant subspace, and in Foias, Jung, Ko, and Pearcy (2008) [5] we proved that the commutant of each of these rank-one perturbations is abelian. In this paper we show that the operators considered in Foias, Jung, Ko, and Pearcy (2007) [4] have more structure - namely, that they are decomposable operators in the sense of Colojoarǎ and Foias (1968) [1].

Original language	English
Pages (from-to)	602-609
Number of pages	8
Journal	Journal of Mathematical Analysis and Applications
Volume	375
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2010.09.037
State	Published - 15 Mar 2011

Bibliographical note

Funding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0087565).

Keywords

Decomposable operator
Hyperinvariant subspace
Invariant subspace
Normal operator
Rank-one perturbation

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title = "Spectral decomposability of rank-one perturbations of normal operators",

abstract = "This paper is a continuation of the study by Foias, Jung, Ko, and Pearcy (2007) [4] and Foias, Jung, Ko, and Pearcy (2008) [5] of rank-one perturbations of diagonalizable normal operators. In Foias, Jung, Ko, and Pearcy (2007) [4] we showed that there is a large class of such operators each of which has a nontrivial hyperinvariant subspace, and in Foias, Jung, Ko, and Pearcy (2008) [5] we proved that the commutant of each of these rank-one perturbations is abelian. In this paper we show that the operators considered in Foias, Jung, Ko, and Pearcy (2007) [4] have more structure - namely, that they are decomposable operators in the sense of Colojoarǎ and Foias (1968) [1].",

keywords = "Decomposable operator, Hyperinvariant subspace, Invariant subspace, Normal operator, Rank-one perturbation",

author = "C. Foias and Jung, {I. B.} and E. Ko and C. Pearcy",

note = "Funding Information: This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0087565).",

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AU - Foias, C.

AU - Jung, I. B.

AU - Ko, E.

AU - Pearcy, C.

N1 - Funding Information: This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009-0087565).

PY - 2011/3/15

Y1 - 2011/3/15

N2 - This paper is a continuation of the study by Foias, Jung, Ko, and Pearcy (2007) [4] and Foias, Jung, Ko, and Pearcy (2008) [5] of rank-one perturbations of diagonalizable normal operators. In Foias, Jung, Ko, and Pearcy (2007) [4] we showed that there is a large class of such operators each of which has a nontrivial hyperinvariant subspace, and in Foias, Jung, Ko, and Pearcy (2008) [5] we proved that the commutant of each of these rank-one perturbations is abelian. In this paper we show that the operators considered in Foias, Jung, Ko, and Pearcy (2007) [4] have more structure - namely, that they are decomposable operators in the sense of Colojoarǎ and Foias (1968) [1].

AB - This paper is a continuation of the study by Foias, Jung, Ko, and Pearcy (2007) [4] and Foias, Jung, Ko, and Pearcy (2008) [5] of rank-one perturbations of diagonalizable normal operators. In Foias, Jung, Ko, and Pearcy (2007) [4] we showed that there is a large class of such operators each of which has a nontrivial hyperinvariant subspace, and in Foias, Jung, Ko, and Pearcy (2008) [5] we proved that the commutant of each of these rank-one perturbations is abelian. In this paper we show that the operators considered in Foias, Jung, Ko, and Pearcy (2007) [4] have more structure - namely, that they are decomposable operators in the sense of Colojoarǎ and Foias (1968) [1].

KW - Decomposable operator

KW - Hyperinvariant subspace

KW - Invariant subspace

KW - Normal operator

KW - Rank-one perturbation

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EP - 609

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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ER -

Spectral decomposability of rank-one perturbations of normal operators

Abstract

Bibliographical note

Keywords

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