Norm Estimates for Solutions of Polynomial Operator Equations

Abstract

We consider the equations ∑k=0mcm-kAkXBk=C and ∑k=0mcm-kAkXBm-k=C, where ck∈C (k=1,…,m), c0=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.