CHARACTERIZATION OF ALUTHGE TRANSFORM OF COMPOSITION OPERATORS

Let \simC φ be the Aluthge transform of composition operator on L^2 (Σ). The main result of this paper is characterizations of Aluthge transform of composition operators in some operator classes that are weaker than hyponormal, such as hyponormal, quasihyponormal, paranormal, ∗-paranormal on L^2 (Σ). Moreover, to explain the results, we provide several useful related examples to show that \simC φ lie between these classes.