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Riccati Equation and Positivity of Operator Matrices
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  • Journal title : Kyungpook mathematical journal
  • Volume 49, Issue 4,  2009, pp.595-603
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2009.49.4.595
 Title & Authors
Riccati Equation and Positivity of Operator Matrices
Fujii, Jun Ichi; Fujii, Masatoshi; Nakamoto, Ritsuo;
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We show that for an algebraic Riccati equation , its solutions are given by X = W + BT for some solution W of = . To generalize this, we give an equivalent condition for for given positive operators B and A, by which it can be regarded as Riccati inequality . As an application, the harmonic mean B ! C is explicitly written even if B and C are noninvertible.
Riccati equation;operator matrix;geometric mean and harmonic mean;
 Cited by
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