Unbounded composition operators on Orlicz spaces

Abstract: In this paper we deal with unbounded composition operators defined in Orlicz spaces. Indeed, we provide some necessary and sufficient condition for densely definedness of composition operators on Orlicz spaces. Also, we will investigate the adjoint of densely defined composition operators and we give some equivalent conditions for it to be densely defined. In addition, we show that densely defined composition operator is continuous if and only if it is everywhere defined. Finally, we characterize densely defined continuous composition operators.