Let \(X\) be a Banach space. Given a family of (not necessarily bounded) operators on \(X\), \(\{A(s):s\in\mathbb{R}\}\). We can define an operator \(\mathcal A\) on \(C_0(\mathbb{R},X)\) by \[ ({\mathcal A})(s)= A(s)f(s)\quad\text{for}\quad f\in D({\mathcal A})\quad\text{and} \quad s\in\mathbb{R}, \] for a suitable definition of the domain \(D({\mathcal A})\). Such an operator is called an operator multiplier. The main aim of this paper is to study such objects and determine necessary and sufficient conditions for such an operator to be the generator of a strongly continuous semigroup.