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자연과학대학
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Journal papers
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On rank-one perturbations of normal operators
Title
On rank-one perturbations of normal operators
Authors
Foias C.
;
Jung I.B.
;
Ko E.
;
Pearcy C.
Ewha Authors
고응일
SCOPUS Author ID
고응일
Issue Date
2007
Journal Title
Journal of Functional Analysis
ISSN
0022-1236
Citation
Journal of Functional Analysis vol. 253, no. 2, pp. 628 - 646
Indexed
SCI; SCIE; SCOPUS
Document Type
Article
Abstract
This paper is concerned with operators on Hilbert space of the form T = D + u ⊗ v where D is a diagonalizable normal operator and u ⊗ v is a rank-one operator. It is shown that if T ∉ C 1 and the vectors u and v have Fourier coefficients {αn}n = 1∞ and {βn}n = 1∞ with respect to an orthonormal basis that diagonalizes D that satisfy ∑n = 1∞ (| αn |2 / 3 + | βn |2 / 3) < ∞, then T has a nontrivial hyperinvariant subspace. This partially answers an open question of at least 30 years duration. © 2007 Elsevier Inc. All rights reserved.
DOI
10.1016/j.jfa.2007.09.007
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