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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.)
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