Iterated Aluthge transforms of composition operators on H2

Sungeun Jung, Yoenha Kim, Eungil Ko

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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
Issue number10
StatePublished - 29 Sep 2015


  • Aluthge transform
  • Composition operator
  • iterated Aluthge transform
  • weighted composition operator


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