Inequalities for the eigenvalues of non-selfadjoint Jacobi operators

DOI10.1007/s11785-009-0040-2zbMath1222.47039arXiv0901.1725OpenAlexW2110071196MaRDI QIDQ537665

Guy Katriel, Marcel Hansmann

Publication date: 20 May 2011

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.1725

zbMATH Keywords

eigenvaluesLieb-Thirring inequalitiesBlaschke-type conditions for analytic functionsnon-selfadjoint Jacobi operatorsperturbation determinant

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Eigenvalue problems for linear operators (47A75) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (16)

Volterra-type discrete integral equations and spectra of non-self-adjoint Jacobi operators ⋮ Variation of discrete spectra for non-selfadjoint perturbations of selfadjoint operators ⋮ On the distribution of the discrete spectrum of nuclearly perturbed operators in Banach spaces ⋮ Lieb-Thirring inequalities for complex finite gap Jacobi matrices ⋮ Some remarks on upper bounds for Weierstrass primary factors and their application in spectral theory ⋮ On quantitative bounds on eigenvalues of a complex perturbation of a Dirac operator ⋮ An eigenvalue estimate and its application to non-selfadjoint Jacobi and Schrödinger operators ⋮ Mini-workshop: Reflectionless operators: the Deift and Simon conjectures. Abstracts from the mini-workshop held October 22--28, 2017 ⋮ Absence of eigenvalues of non-selfadjoint Schrödinger operators on the boundary of their numerical range ⋮ On a sum rule for Schrödinger operators with complex potentials ⋮ Spectral properties of some complex Jacobi matrices ⋮ A Blaschke-type condition for analytic functions on finitely connected domains. Applications to complex perturbations of a finite-band selfadjoint operator ⋮ Counting eigenvalues of Schrödinger operators with fast decaying complex potentials ⋮ On Lieb-Thirring inequalities for one-dimensional non-self-adjoint Jacobi and Schrödinger operators ⋮ Perturbation determinants and discrete spectra of semi-infinite non-self-adjoint Jacobi operators ⋮ Blaschke-type conditions on unbounded domains, generalized convexity, and applications in perturbation theory

Cites Work

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• On the discrete spectrum of non-selfadjoint operators
• Non-self-adjoint Jacobi matrices with a rank-one imaginary part
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• Notes on infinite determinants of Hilbert space operators
• Sum rules for Jacobi matrices and their applications to spectral theory
• Lieb-Thirring inequalities for Jacobi matrices
• Lieb--Thirring bounds for complex Jacobi matrices
• Discrete spectrum for complex perturbations of periodic Jacobi matrices
• A Blaschke-type condition and its application to complex Jacobi matrices
• Complex Jacobi matrices

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