O ct 2 00 2 On the existence of solutions to the operator Riccati equation and the tan Θ theorem
نویسندگان
چکیده
Let A and C be self-adjoint operators such that the spectrum of A lies in a gap of the spectrum of C and let d > 0 be the distance between the spectra of A and C . We prove that under these assumptions the sharp value of the constant c in the condition ‖B‖ < cd implying the solvability of the operator Riccati equation XA−CX+XBX = B∗ is equal to √ 2. We also prove an extension of the Davis-Kahan tanΘ theorem.
منابع مشابه
On the existence of solutions to the operator Riccati equation and the tan Θ theorem
Let A and C be self-adjoint operators such that the spectrum of A lies in a gap of the spectrum of C and let d > 0 be the distance between the spectra of A and C . We prove that under these assumptions the sharp value of the constant c in the condition ‖B‖ < cd implying the solvability of the operator Riccati equation XA−CX+XBX = B∗ is equal to √ 2. We also prove an extension of the Davis-Kahan...
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