In mathematics, the composition operator C ϕ {\displaystyle C_{\phi }} with symbol ϕ {\displaystyle \phi } is a linear operator defined by the rule C ϕ ( f ) = f ∘ ϕ {\displaystyle C_{\phi }(f)=f\circ \phi } where f ∘ ϕ {\displaystyle f\circ \phi } denotes function composition.
The study of composition operators is covered by AMS category 47B33.