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On rank-one perturbations of normal operators, II

Title
On rank-one perturbations of normal operators, II
Authors
Foias C.Jung I.B.Ko E.Pearcy C.
Ewha Authors
고응일
SCOPUS Author ID
고응일scopus
Issue Date
2008
Journal Title
Indiana University Mathematics Journal
ISSN
0022-2518JCR Link
Citation
vol. 57, no. 6, pp. 2745 - 2760
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
AS the title indicates, this note is a sequel to [2], in which we showed that a large class of rank-one perturbations of a diagonalizable normal operator have nontrivial hyperinvariant subspaces. Below we establish the perhaps surprising fact that the commutants of such operators are abelian, paralleling thereby the properties of the commutants of normal operators of multiplicity one. We also show by example that this behavior does not extend to the commutants of rank-one perturbations of all normal operators of multiplicity one, and we discuss similarity and quasisimilarity questions associated with this class of operators.
DOI
10.1512/iumj.2008.57.3749
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자연과학대학 > 수학전공 > Journal papers
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