Norm controlled inversions and a corona theorem for \(H^\infty \)-quotient algebras

DOI10.1016/j.jfa.2008.05.011zbMath1161.46028OpenAlexW2063815808MaRDI QIDQ941411

Pamela Gorkin, Nikolai Nikolski, Raymond Mortini

Publication date: 1 September 2008

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

Full work available at URL: https://doi.org/10.1016/j.jfa.2008.05.011

zbMATH Keywords

inner functionsweak embedding property\(H^{\infty }\)-calculus\(H^{\infty }\)-quotient algebrascorona theoremsmodel operatorsnorm estimates of corona-solutions

Mathematics Subject Classification ID

Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) Spaces of bounded analytic functions of one complex variable (30H05)

Related Items (13)

Invertibility Threshold for Nevanlinna Quotient Algebras ⋮ A characterization of the Schur property through the disk algebra ⋮ Weak embedding property, inner functions and entropy ⋮ Two new characterizations of Carleson-Newman Blaschke products ⋮ From \(\mathcal{H}^\infty\) to \(\mathcal{N}\). Pointwise properties and algebraic structure in the Nevanlinna class ⋮ Paths of inner-related functions ⋮ Generalized Carleson-Newman inner functions ⋮ Numerically detectable hidden spectrum of certain integration operators ⋮ The Corona property in Nevanlinna quotient algebras and interpolating sequences ⋮ A new class of inner functions uniformly approximable by interpolating Blaschke products ⋮ The spectral localization property for diagonal operators and semigroups ⋮ Invertibility threshold for $H^{∞}$ trace algebras, and effective matrix inversions ⋮ Reducibility of function pairs in $H^\infty _{\mathbb R}$

Cites Work

• Two new characterizations of Carleson-Newman Blaschke products
• A function model and some problems in the spectral theory of functions
• Sums of invariant subspaces
• In search of the invisible spectrum
• An interpolation problem for subalgebras of \(H^ \infty\)
• Bounded analytic functions and Gleason parts
• The matrix-valued \(H^p\) Corona problem in the disk and polydisk
• Algebras of Bounded Analytic Functions containing the Disk Algebra
• Condition numbers of large matrices, and analytic capacities
• Some Lemmas on Interpolating Blaschke Products and a Correction
• Sequence spaces of continuous functions
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