The boundedness, closed range, invertibility, compactness and closedness of multiplication operators on Orlicz-Lorentz spaces are characterized in this paper.

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In a self-contained presentation, we discuss the Orlicz-Lorentz space. Also the boundedness of composition operators on Orlicz-Lorentz spaces are characterized in this paper.

Abstract. The boundedness, compactness, closed range and invertibility of the weighted composition operator on two-dimensional Lorentz spaces are characterized.Mathematics subject classification (2010): Primary 47B33, 47B38, Secondary 46E30.

The boundedness, compactness and closed range of the multiplication operator defined on mixed norm Lebesgue spaces are characterized in this paper.