Viewing *-multiplication operators between Orlicz spaces

Abstract

In this paper, Lambert multipliers acting between Orlicz spaces are characterized based on some properties of conditional expectation operators. We provide a necessary and sufficient condition for the *-multiplication operators to have closed range. Finally, a necessary condition for Fredholmness of these type of operators will be investigated.

Some results on linear operators: Norm equivalence and closed range

“…The closed range of some specific operators has also been of interest. For example, the closed range of * -multiplication operators defined on L P and Orlicz spaces which was characterized in [4,5], and also the closed range of multiplication operators defined on Orlicz spaces and weighted composition operators acting on multidimensional Lorentz spaces, which was studied in [2,3].…”