= Star polynomial in one normal element
{title2=$\sum_{j,k}c_{jk}x^j(x^*)^k$}
= Star polynomials in one normal element
{synonym}
Since a <normal C-star element> commutes with its adjoint, words in those two generators can be rearranged into the displayed finite sum. Including the constant term generates the unital star algebra; omitting it generates the nonunital star algebra. Under <continuous functional calculus>, such a sum is the ordinary function $\sum_{j,k}c_{jk}z^j\overline z^k$ on the spectrum. The <Stone-Weierstrass theorem> makes these functions uniformly dense.
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