On the optimal reconstruction of the values of operators

Abstract

For a continuous operator $А:\; X \rightarrow Y,$ we formulate the problem of the optimal renewal of values $Аx,\; x \in X$ by decreasing the uncertainty domain by using an information $\mu_k(x),\; k = 1, 2, ...,$, where $\mu_k$ are continuous functionals, defined on the space $X$. Specific results are obtained for some integral operators in functional spaces.