Curvatures and Similarity of Operators with Holomorphic Eigenvectors

DOI10.2307/2001351zbMath0733.47015OpenAlexW4248973090MaRDI QIDQ3359242

Mitsuru Uchiyama

Publication date: 1990

Full work available at URL: https://doi.org/10.2307/2001351

zbMATH Keywords

curvaturewhat operators are similar or quasi-similar to the shifts

Mathematics Subject Classification ID

Structure theory of linear operators (47A65) Canonical models for contractions and nonselfadjoint linear operators (47A45) (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces (47A70)

Related Items (18)

Holomorphic spectral theory: a geometric approach ⋮ An Introduction to Hilbert Module Approach to Multivariable Operator Theory ⋮ Applications of Hilbert Module Approach to Multivariable Operator Theory ⋮ On quasi-affinity and reducing subspaces of multiplication operator on a certain closed subspace ⋮ Curvature inequalities for operators of the Cowen-Douglas class ⋮ The trace of the curvature determines similarity ⋮ Notes on the codimension one conjecture in the operator corona theorem ⋮ Curvature invariant and generalized canonical operator models. II ⋮ On a generalization of \(B_1(\Omega)\) on \(C^\ast\)-algebras ⋮ Contractive Hilbert modules and their dilations ⋮ Similarity of quotient Hilbert modules in the Cowen-Douglas class ⋮ Confluent operator algebras and the closability property ⋮ Similarity of operators and geometry of eigenvector bundles ⋮ On the properties of canonical solution operator to \({\bar{\partial }}\) restricted to Dirichlet space ⋮ Curvature formulas of holomorphic curves on \(C^*\)-algebras and Cowen-Douglas operators ⋮ Curvature inequalities and extremal operators ⋮ On the norm of Hankel operator restricted to Fock space ⋮ Curvature Invariant and Generalized Canonical Operator Models – I

Cites Work

• A corona theorem for countably many functions
• Contraction Operators Quasisimilar to a Unilateral Shift
• Curvature and the Backward Shift Operators
• On Quasiaffine Transforms of Unilateral Shifts
• On contractions similar to isometries and Toeplitz operators
• Essential Spectra of Operators in the Class B n (Ω)
• On the Corona Theorem and its Application to Spectral Problems in Hilbert Space
• Complex geometry and operator theory
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