Relevant for questions related to Koopman operator, also known as the Composition operator. It's is a linear operator that describes the evolution of scalar observables (i.e., measurement functions of the states) in an infinite-dimensional Hilbert space.
In mathematics, the composition operator (usually referred to as the Koopman operator) $C_\phi$ with symbol $\phi$ is a linear operator defined by the rule $$\displaystyle C_{\phi }(f)=f\circ \phi $$ where $f\circ \phi$ denotes function composition.