Norm Estimates for Solutions of Polynomial Operator Equations

Abstract EN

We consider the equations ∑ k = 0 m c m - k A k X B k = C and ∑ k = 0 m c m - k A k X B m - k = C , where c k ∈ C ( k = 1 , … , m ) , c 0 = 1 , A , B , C are given linear bounded operators in a Banach space and X is to be found.

Representations of solutions are derived.

In the cases of Euclidean and Hilbert spaces, norm estimates for the solutions are suggested.