Basic properties of multiplication and composition operators between distinct Orlicz spaces

Abstract

First, we present some simple (and easily verifiable) necessary conditions and sufficient conditions for boundedness of the multiplication operator M u and composition operator C T acting from Orlicz space L 1 () into Orlicz space L 2 () over arbitrary complete, σ-finite measure space (, , μ). Next, we investigate the problem of conditions on the generating Young functions, the function u, and/or the function h = d(μ • T −1)/dμ, under which the operators M u and C T are of closed range or finite rank. Finally, we give necessary and sufficient conditions for boundedness of the operators M u and C T in terms of techniques developed within the theory of Musielak-Orlicz spaces.

Surjectivity, Closed Range, and Fredholmness of the Composition and Multiplication Operators Between Possibly Distinct Orlicz Spaces

“…We continue our investigation of the composition and multiplication operators between possibly different Orlicz spaces over non-atomic measure spaces. It was initiated in the papers [1,2] (see also [16]). For results on the composition and multiplication operators between the same Orlicz spaces, see, e.g.…”

Multiplication operators on non-commutative spaces

“…In recent years there appears to be a renewed interest in the study of multiplication operators. Even in the commutative setting new results regarding multiplication operators on Orlicz spaces [6,7], Orlicz-Lorentz sequence spaces [2] and Köthe sequence spaces [26] have recently been obtained. In the noncommutative setting, multiplication operators have been studied on von Neumann algebras and their preduals, and between distinct Orlicz spaces [23].…”