02-413 V. Kostrykin, K. A. Makarov, A. K. Motovilov

On the existence of solutions to the operator Riccati equation and the \tan\Theta theorem (105K, LaTeX2e) Oct 3, 02

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Abstract. 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 \sqrt{2}. We also prove an extension of the Davis-Kahan \tan\Theta theorem.

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