On the order of approximation of continuous functions by positive linear operators of finite rank (Q1190995)

Let \(\Omega\subset[0,1]\) be a set of positive measure. Let \((L_ n)\) be a sequence of positive linear operators from \(C[0,1]\) into \(B(\Omega)\). Suppose that each \(L_ n\) has \((n+1)\)-dimensional range consisting of measurable functions. The authors prove that \(n^ 2\sum^ 2_{j=0}| L_ n(t^ j;x)-x^ j|\) does not tend to zero, almost everywhere on \(\Omega\).