Characterization of Aluthge Transform of Composition Operators

Let widetilde{{C}_{varphi}} be the Aluthge transform of composition operator on L^{۲}(Sigma). 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^{۲}(Sigma). Moreover, to explain the results, we provide several useful related examples to show that widetilde{{C}_{varphi}} lie between these classes.

Keywords:

Aluthge transform , polar decomposition , conditional expectation , hyponormal , paranormal