 02413 V. Kostrykin, K. A. Makarov, A. K. Motovilov
 On the existence of solutions to the operator Riccati equation and the \tan\Theta theorem
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Oct 3, 02

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Abstract. Let A and C be selfadjoint 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 XACX+XBX=B^* is equal to \sqrt{2}. We also prove an extension of the DavisKahan \tan\Theta theorem.
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