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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".

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I am wondering which one in this algebra is the canonical generator. Thanks a lot.

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    It's not terminology I've heard before, but it probably doesn't make sense for it to mean anything but the identity function ($f(x)=x$).2012-12-01
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    @Henning Makholm: Thank you very much for the comment. I have add some details, trying to make the question more clear.2012-12-02

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