On the Cauchy dual and complex symmetric of composition operators

In this paper, firstly we show that some classical properties for Cauchy dual and Moore-Penrose inverse of composition operators, such as complex symmetric and Aluthge transform on L2(Σ). Secondly we give a characterization for some operator classes of weak p-hyponormal via Moore-Penrose inverse of composition operators. Finally, some examples are then presented to illustrate that, the Moore-Penrose inverse of composition operators lie between these classes.