ON THE SOLVABILITY OF GENERALIZED SYLVESTER OPERATOR EQUATIONS.

In this paper, some necessary and sufficient solvability conditions are established for the generalized Sylvester operator equations AXB-CXD = E, AXB-CYD = E and AX + YB+CZ = E on Hilbert spaces, respectively. Moreover, we give a solvability condition for the *-Sylvester operator equation AX -X*B = C, which holds for finite matrices due to Wimmer (1994). [ABSTRACT FROM AUTHOR]