On the existence of solutions to the operator Riccati equation and the \(\tan\Theta\) theorem

DOI10.1007/s00020-003-1248-6zbMath1089.47015arXivmath/0210032OpenAlexW2009163511MaRDI QIDQ1772905

Konstantin A. Makarov, Vadim Kostrykin, Alexander K. Motovilov

Publication date: 21 April 2005

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0210032

zbMATH Keywords

invariant subspacesfactorization theoremoperator Riccati equationoperator matrixoperator angle

Mathematics Subject Classification ID

Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Perturbation theory of linear operators (47A55) Invariant subspaces of linear operators (47A15)

Related Items (12)

Alternative proof of the a priori \(\tan \theta\) theorem ⋮ The a priori \(\tan \Theta\) theorem for spectral subspaces ⋮ Maximal \(L^p\)-regularity and \(H^\infty\)-calculus for block operator matrices and applications ⋮ The tan Θ theorem for definite matrix pairs ⋮ Diagonalization of indefinite saddle point forms ⋮ Notes on the \(\sin 2\Theta\) theorem ⋮ Operator Stieltjes integrals with respect to a spectral measure and solutions of some operator equations ⋮ On invariant graph subspaces ⋮ Spectral estimates and basis properties for self-adjoint block operator matrices ⋮ Analytic functional calculus for two operators ⋮ Spectral inclusion for unbounded block operator matrices ⋮ Solvability of the operator Riccati equation in the Feshbach case

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