Solving algebraic and differential Riccati operator equations (Q802839)

Let A,B,C,D,E,F,G,P be bounded operators on a separable Hilbert space. The paper first presents a necessary and sufficient condition under which an algebraic Riccati equation \((1)\quad A+BX-XC-XDX=0\) can be transformed in a linear system \(M+XN=0,\quad R+XS=0.\) If a solution \(X_ 0\) of (1) is known, the author derives two analytic formulae, one for an operator U such that \(X=U+X_ 0\) solves a Cauchy problem \(\dot X=A+BX-XC-XDX,\quad X(0)=P,\) the other for a solution of a boundary-value problem \(\dot X=A+BX-XC-XDX,\quad EX(b)-X(0)F=G\).