An eigenvalue estimate and its application to non-selfadjoint Jacobi and Schrödinger operators

Abstract

For bounded linear operators $A,B$ on a Hilbert space $\mathcal{H}$ we show the validity of the estimate $$ \sum_{λ\in σ_d (B)} \dist(λ, \overline{\num}(A))^p \leq \| B-A \|_{\mathcal{S}_p}^p$$ and apply it to recover and improve some Lieb-Thirring type inequalities for non-selfadjoint Jacobi and Schrödinger operators.

References in corpus (4)

• Eigenvalue bounds for Schrödinger operators with complex potentials
• Lieb-Thirring inequalities for Schrödinger operators with complex-valued potentials
• A Blaschke-type condition and its application to complex Jacobi matrices
• Lieb-Thirring estimates for non self-adjoint Schrödinger operators

Cited by in corpus (10)

• Variation of discrete spectra for non-selfadjoint perturbations of selfadjoint operators
• Trace formulas for Schrödinger operators with complex potentials on half-line
• Trace formulas for Schrödinger operators on periodic graphs
• Stability of linear GMRES convergence with respect to compact perturbations
• $L_p$-spectrum and Lieb-Thirring inequalities for Schrödinger operators on the hyperbolic plane
• Lieb-Thirring Inequalities for Complex Finite Gap Jacobi Matrices
• Notes on Lieb-Thirring type inequality for a complex perturbation of fractional Schrödinger operator
• Absence of eigenvalues of non-selfadjoint Schrödinger operators on the boundary of their numerical range
• On quantitative bounds on eigenvalues of a complex perturbation of a Dirac operator
• On Lieb-Thirring inequalities for multidimensional Schrödinger operators with complex potentials