On the generalized Sylvester operator equation AX − Y B = C
Il Ju An, Eungil Ko, Ji Eun Lee · Linear and Multilinear Algebra · 2022
In this paper, we study the necessary and sufficient conditions to have a solution pair (X,Y) to the generalized Sylvester equation AX−Y B = C where A,B,C∈L(H) are given. Moreover, we give some connections the generalized Fuglede-Putnam property and the solution pair (X,Y) 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.