Composition operator

In mathematics, the composition operator ${\displaystyle C_{\phi }}$ with symbol ${\displaystyle \phi }$ is a linear operator defined by the rule $${\displaystyle C_{\phi }(f)=f\circ \phi }$$ where ${\displaystyle f\circ \phi }$ denotes function composition. It is also encountered in composition of permutations in permutations groups.

The study of composition operators is covered by AMS category 47B33.