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• W2009163511 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. Under these assumptions we prove that the best possible value of the constant c in the condition $$left| B right| < cd$$ guaranteeing the existence of a (bounded) solution to the operator Riccati equation XA−CX+XBX = B* is equal to $$sqrt 2 .$$ We also prove an extension of the Davis-Kahan tan Θ theorem and provide a sharp estimate for the norm of the solution to the Riccati equation. If C is bounded, we prove, in addition, that the solution X is a strict contraction if B satisfies the condition $$left| B right| < d,$$ and that this condition is optimal." @default.
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• W2009163511 date "2005-01-01" @default.
• W2009163511 modified "2023-10-17" @default.
• W2009163511 title "On the Existence of Solutions to the Operator Riccati Equation and the tan ? Theorem" @default.
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• W2009163511 doi "https://doi.org/10.1007/s00020-003-1248-6" @default.
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