Multiplication and composition operators on Orlicz-Lorentz spaces.(English)Zbl 1160.47023

In this paper, the boundedness and invertibility of the multiplication operator $$M_u$$ are characterized in terms of the boundedness and invertibility of the complex-valued measurable function $$u$$, respectively. The paper also presents a necessary and sufficient condition for the composition operator to be bounded on a $$\sigma$$-finite measure space.

MSC:

 47B33 Linear composition operators 47B38 Linear operators on function spaces (general) 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)