Abstract
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.
Original language | English |
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Article number | 1550079 |
Journal | International Journal of Mathematics |
Volume | 26 |
Issue number | 10 |
DOIs | |
State | Published - 29 Sep 2015 |
Bibliographical note
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.
Keywords
- Aluthge transform
- Composition operator
- iterated Aluthge transform
- weighted composition operator