On the existence of solutions to the operator Riccati equation and the tan Θ theorem

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