IUMJ

Title: Hamiltonians with Riesz bases of generalised eigenvectors and Riccati equations

Authors: Christian Wyss

Issue: Volume 60 (2011), Issue 5, 1723-1766

Abstract:

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.