Perturbation of spectra and spectral subspaces

Abstract

We consider the problem of variation of spectral subspaces for linear self-adjoint operators under off-diagonal perturbations. We prove a number of new optimal results on the shift of the spectrum and obtain (sharp) estimates on the norm of the difference of two spectral projections.

References in corpus (2)

• Graph Subspaces and the Spectral Shift Function
• On a Subspace Perturbation Problem

Cited by in corpus (15)

• Bounds on variation of spectral subspaces under J-self-adjoint perturbations
• On the existence of solutions to the operator Riccati equation and the tanΘtheorem
• Representation Theorems for Indefinite Quadratic Forms Revisited
• Notes on the sin2Θ theorem
• Bounds on the spectrum and reducing subspaces of a J-self-adjoint operator
• Maximal $L^p$-regularity and $H^{\infty }$-calculus for block operator matrices and applications
• Bounds on variation of the spectrum and spectral subspaces of a few-body Hamiltonian
• Notes on the subspace perturbation problem for off-diagonal perturbations
• On an estimate in the subspace perturbation problem
• Metric properties of the set of orthogonal projections and their applications to operator perturbation theory
• Non-linear eigenvalue problems and applications to photonic crystals
• On applying the subspace perturbation theory to few-body Hamiltonians
• Semidefinite perturbations in the subspace perturbation problem
• The a priori tanθtheorem for eigenvectors
• Applications of fixed point theorems in the theory of invariant subspaces