The disc algebra, as a set, consists of the functions on the unit disc $D$, which are analytic on the interior of the disc and continuous on its boundary. Its addition and multiplication is obvious. And, as a normed algebra, its norm is given by
$\| f\| = \sup\{ |f(z)| | z \in D \}$.
One page 16 of Gerard J. Murphy's C star algebras and Operator Theory, an element in this algebra is called its "canonical generator".
I am wondering which one in this algebra is the canonical generator. Thanks a lot.