On the generalized Sylvester operator equation AX−Y B = C

Abstract

In this paper, we study the necessary and sufficient conditions to have a solution pair (Formula presented.) to the generalized Sylvester equation AX−Y B = C where (Formula presented.) are given. Moreover, we give some connections the generalized Fuglede-Putnam property and the solution pair (Formula presented.) of the operator equation AX−Y B = C. Finally, we consider some properties of the operator equation AX−Y B = C when A and B belong to the special classes of operators. © 2022 Informa UK Limited, trading as Taylor & Francis Group.