Similarity of operators and geometry of eigenvector bundles

DOI10.5565/PUBLMAT_53209_06zbMath1190.47002arXiv0712.0114OpenAlexW2004206615MaRDI QIDQ2271355

Hyun-Kyoung Kwon, S. R. Treil'

Publication date: 7 August 2009

Published in: Publicacions Matemàtiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0712.0114

zbMATH Keywords

similarityreproducing kernelCarleson measurebackward shiftcurvature of the eigenvector bundle

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Spectrum, resolvent (47A10) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32) Hardy spaces (30H10)

Related Items (16)

On the trace of curvature of irreducible Cowen-Douglas operators ⋮ Holomorphic spectral theory: a geometric approach ⋮ Applications of Hilbert Module Approach to Multivariable Operator Theory ⋮ Canonical Models for Bi-isometries ⋮ Factorization of generalized holomorphic curve and homogeneity of operators ⋮ A subclass of the Cowen–Douglas class and similarity ⋮ The trace of the curvature determines similarity ⋮ Geometric similarity invariants of Cowen-Douglas operators ⋮ Curvature invariant and generalized canonical operator models. II ⋮ \(N\)-hypercontractivity and similarity of Cowen-Douglas operators ⋮ A note on curvature and similarity of some Cowen-Douglas operators ⋮ On a generalization of \(B_1(\Omega)\) on \(C^\ast\)-algebras ⋮ Similarity of quotient Hilbert modules in the Cowen-Douglas class ⋮ A note on a subclass of Cowen-Douglas operators ⋮ Curvature condition for non-contractions does not imply similarity to the backward shift ⋮ Curvature formulas of holomorphic curves on \(C^*\)-algebras and Cowen-Douglas operators

Cites Work

• The corona theorem for matrices
• Lower bounds in the matrix corona theorem and the codimension one conjecture
• Interpolations by bounded analytic functions and the corona problem
• Analytic projections, Corona problem and geometry of holomorphic vector bundles
• Curvatures and Similarity of Operators with Holomorphic Eigenvectors
• Unconditional bases of invariant subspaces of a contraction with finite defects
• An operator corona theorem
• Complex geometry and operator theory
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