SOLUTION OF OPERATOR EQUATIONS
Abstract
In this paper, we study and discuss the existence and uniqueness of the solution of the discrete –time Sylvester and Lyapunov operator equations, and more general continuous –time Lyapunovoperator equations. Also, we study the nature of the solution for these operator equation for specialtypes of operators, as well as the study of the range A,B, A,and tA are introduced.Where,A,B(x)=AX-XB-1A(x)=A*X-XA-1, andtA(x)= A*X+tXA, XB(H).for A,B-1and A-1 are fixed operators in B(H),and t is any scalar.
Keywords
Lyapunov equation, Sylvester Equation, Discrete-time operator equation and continuous-time operator equationMetrics