[Nontrivial F] (T T' : F →L[ℂ] F) (hT : IsSelfAdjoint T) (hT' : IsSelfAdjoint T') (hne : (minmaxSet T 0).Nonempty) : |sInf (spectrum ℝ T) - sInf (spectrum ℝ T')| ≤ ‖T - T'‖
OpenBookProof.RitzPerturbation.abs_sInf_spectrum_sub_le_disttimepiece
Lean 4 theorem BookProof.RitzPerturbation.abs_sInf_spectrum_sub_le_dist (module BookProof.RitzPerturbation), source chapter BookProof/ChapterRitzPerturbation.lean.
Preamble
-- Generated from ChapterSirkRitzPerturbation.lean — theorem BookProof.RitzPerturbation.abs_sInf_spectrum_sub_le_dist
import Mathlib
import Definitions.Def_ChapterSirkRitzPerturbation
open BookProof.RitzPerturbation
noncomputable section
open BookProof.RitzMinMax BookProof.ChapterSirkRitzSpectrum BookProof.HermiteGalerkin
open Filter Topology
variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] [CompleteSpace F]Formal statement
theorem BookProof.RitzPerturbation.abs_sInf_spectrum_sub_le_dist [Nontrivial F] (T T' : F →L[ℂ] F)
(hT : IsSelfAdjoint T) (hT' : IsSelfAdjoint T')
(hne : (minmaxSet T 0).Nonempty) :
|sInf (spectrum ℝ T) - sInf (spectrum ℝ T')| ≤ ‖T - T'‖ := by sorrySource