A SYSTEM OF MIXED SYLVESTER-TYPE OF OPERATOR EQUATIONS

The Sylvester matrix equation and generalized Sylvester matrix equations are interesting problems, hence some authors, by using bloke matrix decomposition in operator theory find exact solutions and obtain conditions solvability, then they apply and generalize in matrix theory and vice versa. However, we present a kind of system of mixed Sylvester-type of operator equations and find the general solutions of them.