TY - JOUR
T1 - Spectral decomposability of rank-one perturbations of normal operators
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
UR - http://www.scopus.com/inward/record.url?scp=78149407572&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2010.09.037
DO - 10.1016/j.jmaa.2010.09.037
M3 - Article
AN - SCOPUS:78149407572
SN - 0022-247X
VL - 375
SP - 602
EP - 609
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -