Solutions of the Operator Equation A*X+XA=B
Tian Xue-gan · Journal of Lanzhou University of Arts and Science · 2015
Let A,Bbe two bounded linear operators on a complex separable Hilbert space H.Using the block operator matrix technique and generalized inverse of operator,when Ais an idempotent or a generalized idempotent operator,the sufficient and necessary conditions for the existence of solutions and self-adjoint solutions of the equation A*X+XA=Band the representations of those solutions are established.