Iterated Aluthge transforms of composition operators on H2

In this paper, we study various properties of the iterated Aluthge transforms of the composition operators Cφ and Cσ where φ(z) = az + (1 - a) and [Formula: see text] for 0 < a < 1. We express the iterated Aluthge transforms [Formula: see text] and [Formula: see text] as weighted composition operators with linear fractional symbols. As a corollary, we prove that [Formula: see text] and [Formula: see text] are not quasinormal but binormal. In addition, we show that [Formula: see text] and [Formula: see text] are quasisimilar for all non-negative integers n and m. Finally, we show that [Formula: see text] and [Formula: see text] converge to normal operators in the strong operator topology.