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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

Nguyen Thanh Lan

Department of Mathematics, Ohio University, Athens 45701, OH, USA

Received 30 July 2001

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.