  For the L_2-orthogonal projector P onto spaces of linear splines over
simplicial partitions of polyhedral domains in R^d, d>1, we show that the
L_infty norm of P cannot be bounded uniformly with respect to the partition.
This is in contrast to d=1, where these norms are bounded by 3 independently of
the partition. This negative result is folklore among specialists in finite
element methods and approximation theory but seemingly has never been formally
proved.
