Infinite Hankel Block Matrices, Extremal Problems

In the paper we consider a matrix version of the extremal Nehary problem [1],[4]. Our approach is based on the notion of a matrix analogue of the eigenvalue ρ2min. The notion of ρ 2 min was used in a number of the extremal interpolation problems [2],[3],[7]. We note that ρ2min is a solution of a nonlinear matrix inequality of the Riccati type [2],[6], [7]. Our approach coincides with the Adamjan-Arov-Krein approach [1], when ρ2min is a scalar matrix. Now we introduce the main definitions. Let H be a fixed separable Hilbert space. By l2(H) we denote the Hilbert space of the sequences ξ = {ξk} ∞ 1 , where ξk∈H and ‖ξ‖ = ∞