Nonsummability of almost everywhere orthorecursive expansions

It was proved earlier that only Weyl multiplier $\lambda_k$ with the property $\sum\limits_{k=1}^\infty \frac1{\lambda_k}<\infty$ provides the almost every where convergence of an orthorecurcive expansions of a function which does not converge to it in the norm. This result is extended to summation methods that sum a sequence being constant staring with some its element to its limit.