Optimal recovery of mappings, optimal information operators, and extremal subspaces - Babenko, V.; Babenko, Yu.; Parfinovych, N. (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 517.5 We consider the problems of optimal recovery of an operator A (generally speaking, nonlinear) defined on a unit ball B_H of the Hilbert space H based on the information about elements of this unit ball B_H given by a linear bounded operator TH→ Y, where Y is a Banach space. For a fixed information operator T, it is shown that the optimal method of recovery is offered by the so-called T-interpolating splines. For a fixed Y we also solve the problem of finding the optimal information operator. Moreover, for a bounded linear self-adjoint operator A, it is shown that if T is the optimal information operator for the recovery of A on B_H, then any other operator TA^n, nN, is also an optimal information operator.