A Spectral Commutant Lifting Theorem

DOI10.2307/2001646zbMath0738.47006OpenAlexW4248181945MaRDI QIDQ3978441

Hari Bercovici, Ciprian Foias, Allen Tannenbaum

Publication date: 25 June 1992

Full work available at URL: https://doi.org/10.2307/2001646

zbMATH Keywords

spectral radiusdilation theoryclassical Nevanlinna-Pick interpolation problemspectral version of commutant lifting theorem

Mathematics Subject Classification ID

Linear systems in control theory (93C05) Linear operator methods in interpolation, moment and extension problems (47A57) Dilations, extensions, compressions of linear operators (47A20) Moment problems and interpolation problems in the complex plane (30E05)

Related Items (22)

The hyperbolic geometry of the symmetrized bidisc ⋮ A Schwarz lemma for the symmetrized polydisc via estimates on another family of domains ⋮ Bitangential structured interpolation theory ⋮ Lifting to the spectral ball with interpolation ⋮ A Cartan theorem for Banach algebras ⋮ A refined Schwarz lemma for the spectral Nevanlinna-Pick problem ⋮ On spectral tangential Nevanlinna-Pick interpolation ⋮ The invariant subspaces of a uniform Jordan operator ⋮ Spectral lifting in Banach algebras and interpolation in several variables ⋮ A rich structure related to the construction of analytic matrix functions ⋮ A Schwarz lemma for a domain related to \(\mu\)-synthesis ⋮ The fibred density property and the automorphism group of the spectral ball ⋮ Quasiaffine orbits of invariant subspaces for uniform Jordan operators ⋮ The two-by-two spectral Nevanlinna-Pick problem ⋮ The 3-point spectral Pick interpolation problem and an application to holomorphic correspondences ⋮ A commutant lifting theorem for a domain in \(\mathbb{C}^2\) and spectral interpolation ⋮ On the automorphisms of the spectral unit ball ⋮ Some Analysable Instances of μ-synthesis ⋮ Operators having the symmetrized bidisc as a spectral set ⋮ The two-point spectral Nevanlinna--Pick problem. ⋮ A counterexample to the \varGamma -interpolation conjecture ⋮ A family of domains associated with \(\mu\)-synthesis

Cites Work

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• A course in \(H_{\infty}\) control theory
• A maximum entropy principle for contractive interpolants
• Generalized interpolation in control theory
• Invariance and system theory: algebraic and geometric aspects
• On models for linear operators
• Infinite Hankel block matrices and related extension problems
• Generalized Interpolation in H ∞

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