Existence and Uniqueness of Solutions to the Operator Riccati Equation. a Geometric Approach
نویسنده
چکیده
We introduce a new concept of unbounded solutions to the operator Riccati equation A1X − XA0 − XV X + V ∗ = 0 and give a complete description of its solutions associated with the spectral graph subspaces of the block operator matrix B = ( A0 V V ∗ A1 ) . 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.
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