Approximation by linear methods of summation of orthogonal series

We give an estimate of the rapidity of convergence of certain linear means of the orthogonal series $\sum_{k=0}^\infty c_k\varphi_k(x)$ to the function $f(x)\in L_2(a,b)$ defined by this series according to the Riesz-Fisher theorem for almost all $x\in(a,b)$. The results obtained are, in a certain sense, final.