Multiplication Operators on Generalized Orlicz Spaces Associated to Banach Function Spaces

In this paper, we study multiplication operators on generalized Orlicz spaces \(X^\Phi\) $X^{\mathrm{\Phi }}$ associated to a Banach function space X, where \(\Phi\) $\mathrm{\Phi }$ is a Young function, and give some characterization of them to be well-defined and bounded. Also, we present some sufficient and necessary conditions for such operators to be compact or invertible. Moreover, we find the essential norm of a multiplication operator on \(X^\Phi\) $X^{\mathrm{\Phi }}$ while the context measure space is discrete. Many results of this paper cover known Banach function spaces related to Orlicz one.