Existence and uniqueness of contractive solutions of some Riccati equations

DOI10.1006/jfan.2000.3680zbMath0982.47019OpenAlexW1993453399MaRDI QIDQ5927520

Christiane Tretter, Heinz K. Langer, Vadim Adamjan

Publication date: 20 March 2001

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.2000.3680

zbMATH Keywords

Hamiltoniancontractive solutionsindefinite inner productinvariance subspaceKrein spaceRiccati equations

Mathematics Subject Classification ID

Invariant subspaces of linear operators (47A15) Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) (46C20) Equations involving linear operators, with operator unknowns (47A62)

Related Items (18)

Asymptotic behaviour of solutions of Lotka-Volterra systems ⋮ A representation of all solutions of the control algebraic Riccati equation for infinite-dimensional systems ⋮ Reflection positivity via Krein space analysis ⋮ Applications of fixed point theorems in the theory of invariant subspaces ⋮ The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits ⋮ Multi-photon Rabi model: generalized parity and its applications ⋮ On the solution of nonlinear operator equations and the invariant subspace ⋮ The \(\operatorname{Tan}2\Theta \) theorem for indefinite quadratic forms ⋮ Diagonalization of indefinite saddle point forms ⋮ On applications of Schauder's fixed-point theorem for the solution of the non-symmetric algebraic Riccati equation ⋮ Operator Stieltjes integrals with respect to a spectral measure and solutions of some operator equations ⋮ On invariant graph subspaces ⋮ On the Riccati equations ⋮ Dichotomous Hamiltonians with unbounded entries and solutions of Riccati equations ⋮ On some problems for reproducing kernel Hilbert space operators via the Berezin transform ⋮ Solvability of the operator Riccati equation in the Feshbach case ⋮ Perturbation of spectra and spectral subspaces ⋮ Riccati equation and the problem of decoherence

Cites Work

• Classes of linear operators. Vol. I
• Operator Interpretation of Resonances Arising in Spectral Problems for 2 × 2 Operator Matrices
• Analysis and modificaton of Newton’s method for algebraic Riccati equations
• Removal of the resolvent-like energy dependence from interactions and invariant subspaces of a total Hamiltonian
• Spectral Components of Selfadjoint Block Operator Matrices with Unbounded Entries
• Interpolation zwischen den Klassen 𝔖_p von Operatoren in Hilberträumen
• Über die Methode der richtenden Funktionale von M. G. Krein
• A new concept for block operator matrices: The quadratic numerical range
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Existence and uniqueness of contractive solutions of some Riccati equations