Let $(X,\mathcal{A},\mu)$ be a measure space and $f \colon X \to \mathbb{K}$ a measurable function. Then $M_f \colon \phi \mapsto f \phi$ is the multiplication operator with $f$ defined on the subspace $Dom(M_f)=\{\phi \in L^2_\mathbb{K}(X,\mathcal{A},\mu) \colon f \phi \in L^2_\mathbb{K}(X,\mathcal{A},\mu)\}$ It plays an important role in quantum mechanics where the multiplication with the coordinates on $\mathbb{R}^n$ is the position operator.