On optimal recovery in $L_2$

We prove that the optimal error of recovery in the $L_2$ norm of functions from a class $\text{bF}$ can be bounded above by the value of the Kolmogorov width of $\text{bF}$ in the uniform norm. We demonstrate on a number of examples of $\text{bF}$ from classes of functions with mixed smoothness that the obtained inequality provides a powerful tool for estimating errors of optimal recovery.