Article
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
Document Type
Article
Publication Date
4-1-1990
Disciplines
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 (*).
DOI
10.1216/rmjm/1181073122
Citation Information
Tapas Mazumdar and David Miller. "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 Vol. 20 Iss. 2 (1990) p. 475 - 486 ISSN: 0035-7596 Available at: http://works.bepress.com/david_miller/1/