Hamiltonians with Riesz bases of generalised eigenvectors and Riccati equations Christian Wyss 47A6247A1547A7047B5047N70Riccati equationHamiltonian operator matrixRiesz basis of generalised eigenvectorsinvariant subspaceindefinite inner product An algebraic Riccati equation for linear operators, which arises in systems theory, is studied. For the case that all involved operators are unbounded, the existence of infinitely many selfadjoint solutions is shown. The proof uses invariant graph subspaces of the associated Hamiltonian operator matrix, Riesz bases with parentheses of generalised eigenvectors and indefinite inner products. Under additional assumptions, the existence and a representation of all bounded solutions is obtained. The theory is applied to Riccati equations of differential operators. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4407 10.1512/iumj.2011.60.4407 en Indiana Univ. Math. J. 60 (2011) 1723 - 1766 state-of-the-art mathematics http://iumj.org/access/