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Journal d'Analyse Mathématique

, Volume 135, Issue 1, pp 313–343 | Cite as

On an estimate in the subspace perturbation problem

  • Albrecht Seelmann
Article
  • 15 Downloads

Abstract

The problem of variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. The aim is to find the best possible upper bound on the norm of the difference of two spectral projections associated with isolated parts of the spectrum of the perturbed and unperturbed operators. A constrained optimization problem on a specific set of parameters is formulated, whose solution yields an estimate of the arcsine of the norm of the difference of the corresponding spectral projections. The solution is computed explicitly. The corresponding result is stronger than the one obtained by Albeverio and Motovilov and, in fact, is the best possible obtainable using their approach.

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Copyright information

© Hebrew University Magnes Press 2018

Authors and Affiliations

  1. 1.Fakult ät für MathematikTechnische Universität DortmundDortmundGermany

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