TY - JOUR
T1 - Iterated Aluthge transforms of composition operators on H2
AU - Jung, Sungeun
AU - Kim, Yoenha
AU - Ko, Eungil
N1 - Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2009-0083521). In addition, this research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education (No. 2009-0093827). The first author was supported by Hankuk University of Foreign Studies Research Fund.
Publisher Copyright:
© 2015 World Scientific Publishing Company.
PY - 2015/9/29
Y1 - 2015/9/29
N2 - In this paper, we study various properties of the iterated Aluthge transforms of the composition operators Cψ and Cσ where ψ(z) = az + (1-a) and σ(z) + az (1-a)z+1 for 0 < a < 1. We express the iterated Aluthge transforms e C(n) . and C∼ψ(n) as weighted composition operators with linear fractional symbols. As a corollary, we prove that C∼ψ(n) . and C∼ψ(n) are not quasinormal but binormal. In addition, we show that C∼ψ(n) . and e C(m) . are quasisimilar for all non-negative integers n and m. Finally, we show that C∼ψ(n) and C∼ψ(n) converge to normal operators in the strong operator topology.
AB - In this paper, we study various properties of the iterated Aluthge transforms of the composition operators Cψ and Cσ where ψ(z) = az + (1-a) and σ(z) + az (1-a)z+1 for 0 < a < 1. We express the iterated Aluthge transforms e C(n) . and C∼ψ(n) as weighted composition operators with linear fractional symbols. As a corollary, we prove that C∼ψ(n) . and C∼ψ(n) are not quasinormal but binormal. In addition, we show that C∼ψ(n) . and e C(m) . are quasisimilar for all non-negative integers n and m. Finally, we show that C∼ψ(n) and C∼ψ(n) converge to normal operators in the strong operator topology.
KW - Aluthge transform
KW - Composition operator
KW - iterated Aluthge transform
KW - weighted composition operator
UR - http://www.scopus.com/inward/record.url?scp=84942552960&partnerID=8YFLogxK
U2 - 10.1142/S0129167X15500792
DO - 10.1142/S0129167X15500792
M3 - Article
AN - SCOPUS:84942552960
SN - 0129-167X
VL - 26
JO - International Journal of Mathematics
JF - International Journal of Mathematics
IS - 10
M1 - 1550079
ER -