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 -> (1 parallel to x parallel to(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. (C) 2017 Elsevier Inc. All rights reserved.