Abstract and Applied Analysis
Volume 6 (2001), Issue 6, Pages 317-328
doi:10.1155/S1085337501000665
On the operator equation A X−X B=C
with unbounded operators A,B, and C
Department of Mathematics, Ohio University, Athens 45701, OH, USA
Received 30 July 2001
Copyright © 2001 Nguyen Thanh Lan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We find the criteria for the solvability of the operator equation
A X−X B=C, where A,B, and C are unbounded operators, and use the result to show existence and regularity of solutions of nonhomogeneous Cauchy problems.