#### Document Type

Article

#### Publication Date

Spring 1990

#### Abstract

We consider the solution of (*) *XA*+*BX* = *C* for bounded operators *A,B,C* and *X* on a Hilbert space, *A* normal. We establish the existence of a polynomial *p* and a bounded operator *W* with the property that the unique solution *X* of (*) also solves *X − p*(−*B*)*Xp*(*A*)^{−1} = W uniquely. A known iterative algorithm can be applied to the latter equation to solve (*).

#### Repository Citation

Mazumdar, T.,
& Miller, D.
(1990). On the Equivalence of the Operator Equations XA + BX = C and X - p(-B)Xp(A)(-1) = W in a Hilbert-Space, p A Polynomial. *Rocky Mountain Journal of Mathematics, 20* (2), 475-486.

https://corescholar.libraries.wright.edu/math/19

#### DOI

10.1216/rmjm/1181073122