  We study approximation properties of weighted $L^2$-orthogonal projectors
onto spaces of polynomials of bounded degree in the Euclidean unit ball, where
the weight is of the generalized Gegenbauer form $x \mapsto
(1-\|x\|^2)^\alpha$, $\alpha > -1$. Said properties are measured in
Sobolev-type norms in which the same weighted $L^2$ norm is used to control all
the involved weak derivatives. The method of proof does not rely on any
particular basis of orthogonal polynomials, which allows for a short,
streamlined and dimension-independent exposition.
