Existence and uniqueness of solutions to the operator Riccati equation. A geometric approach

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dc.creatorKostrykin, Vadim
dc.creatorMakarov, Konstantin A.
dc.creatorMotovilov, Alexander K.
dc.date2002-07-15
dc.date.accessioned2026-07-07T04:49:41Z
dc.date.available2026-07-07T04:49:41Z
dc.descriptionWe introduce a new concept of unbounded solutions to the operator Riccati equation $A_1 X - X A_0 - X V X + V^\ast = 0$ and give a complete description of its solutions associated with the spectral graph subspaces of the block operator matrix $\mathbf{B} = \begin{pmatrix} A_0 & V V^\ast & A_1 \end{pmatrix}$. 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 $\mathbf{B}$. In this case we establish a criterion for the uniqueness of contractive solutions.
dc.identifierhttps://arxiv.org/abs/math/0207125
dc.identifierhttp://arxiv.org/abs/math/0207125
dc.identifierContemporary Mathematics Vol. 327, Amer. Math. Soc., 2003, p. 181 - 198
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64515
dc.subjectSpectral Theory
dc.subject47A15, 47A55, 47A62 (Primary) 47A53 (Secondary)
dc.titleExistence and uniqueness of solutions to the operator Riccati equation. A geometric approach
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