Solutions to the operator equation AXB~*-BX~*A~*=C
Junlian Xu · Journal of Shandong University · 2012
A∈B(H3,H2),B∈B(H1,H2),while Hi(i=1,2,3) are Hilbert spaces.Using of the technique of block operator matrix,when the range of A is closed and R(B)■R(A),the sufficient and necessary conditions for the existence of solutions to the operator equation AXB*-BX*A*=C and the representation of solutions are established.Especially,when B is an orthogonal projection P,the sufficient and necessary conditions for the existence of solutions to the operator equation AXP-PX*A*=C and the representation of solutions are also given.