2002/07/15 by Vadim Kostrykin, Konstantin A. Makarov, Alexander K. Motovilov
Mathematics · #math.SP #msc:47A15 #msc:47A55 #msc:47A62 #msc:47A53
published as Contemporary Mathematics Vol. 327, Amer. Math. Soc., 2003, p. 181 - 198
arxiv created 2002/07/15 · arxiv updated 2009/11/30
We introduce a new concept of unbounded solutions to the operator Riccati equation A1 X - X A0 - X V X + V^∗ = 0 and give a complete description of its solutions associated with the spectral graph subspaces of the block operator matrix B = \beginpmatrix A0 & V V^∗ & A1 \endpmatrix. We also provide a new characterization of the set of all contractive solutions under the assumption that the Riccati equation has a contractive solution associated with a spectral subspace of the operator B. In this case we establish a criterion for the uniqueness of contractive solutions.