First, define a basic operator on a single variable $x$ and apply it using function notation.

In this example, empty parentheses denote that the operator returns $1$, no matter what the input.

Note that in 1-D Math input, an operator can always be applied by using function notation.  However, in 2-D Math input, when the operator is also of type atomic, you must use the apply command.  This is because $1\left(x\right)$ is interpreted as multiplication in 2-D math rather than function application.  For more information, including how to change this default behavior, see 2DMathDetails.  

Similarly, this multivariate operator returns $3.14$, no matter what the input.

Operators can be applied without assigning them a name.

Operators are distributive.

Use the composition operator @ to perform operator composition.  That is, $f\@g$ means $f\circ g$.

Repeated composition is entered with the @@ operator.  Here, a function is composed with itself.

@, @@, 2-D Math Details, apply, D, Functional Operators, unapply