= Projection in a C-star algebra
{title2=$p=p^*=p^2$}
A projection in a <C-star algebra> is a <Hermitian C-star element> that is also idempotent. Its spectrum is contained in $\{0,1\}$, and a nonzero projection has norm one by the <C-star identity>. If $u$ is a <partial isometry>, $u^*u$ and $uu^*$ are its initial and final projections. For a projection $p$, the closed subalgebra $pAp$ has unit $p$ and the inherited norm and involution; it is the corresponding corner C-star algebra. In an operator representation, such an element acts as an <orthogonal projection>.
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