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

Arora, S. C.; Datt, Gopal; Verma, Satish

Int. J. Math. Anal., Ruse 1, No. 25-28, 1227-1234 (2007).

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.

Reviewer: Zehua Zhou (Tianjin)

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.)

Keywords:

compact operator; composition operator; distribution function; multiplication; non-increasing rearrangement; Orlicz-Lorentz space; Young function