Iterated Aluthge transforms of composition operators on H2

Sungeun Jung, Yoenha Kim, Eungil Ko

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2 Scopus citations

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 Cψ(n) as weighted composition operators with linear fractional symbols. As a corollary, we prove that Cψ(n) . and Cψ(n) are not quasinormal but binormal. In addition, we show that Cψ(n) . and e C(m) . are quasisimilar for all non-negative integers n and m. Finally, we show that Cψ(n) and Cψ(n) converge to normal operators in the strong operator topology.

Original languageEnglish
Article number1550079
JournalInternational Journal of Mathematics
Volume26
Issue number10
DOIs
StatePublished - 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

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