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@inproceedings{Makarov2003OnTE, title={On the existence of solutions to the operator Riccati equation and the tan Θ theorem}, author={K. A. Makarov}, year={2003} }

- Published 2003

Let A andC be self-adjoint operators such that the spectrum of A lies in a gap of the spectrum of C and letd > 0 be the distance between the spectra of A andC. We prove that under these assumptions the sharp value of the constant c in the condition‖B‖< cd guaranteeing the existence of a (bounded) solution to the operator Riccat i equationXA−CX+ XBX= B∗ is… CONTINUE READING