OAI/Analysis/KadisonSimilarity/Representation/SpectralSupportLimit.lean

GitHub source file

6 declarations, 0 contain sorry, 0 declared as axioms

Positive resolvent approximations to the concrete range-support projection. This gives the strong limit needed for the dihedral arc's spectral moments, with operator norm bounded by one throughout.

  1. def OAI.KadisonSimilarity.supportResolvent line 19
  2. theorem OAI.KadisonSimilarity.supportResolvent_norm_le line 22
  3. theorem OAI.KadisonSimilarity.supportResolvent_selfAdjoint line 26
  4. theorem OAI.KadisonSimilarity.supportResolvent_mul_support line 31
  5. theorem OAI.KadisonSimilarity.supportResolvent_range_error line 39
  6. theorem OAI.KadisonSimilarity.supportResolvent_tendsto line 53

    Source documentation

    The positive resolvents converge strongly to the actual range projection.

    theorem supportResolvent_tendsto (B : H →L[ℂ] H) (hB : 0 ≤ B)
    (ε : ℕ → ℝ) (hε : ∀ n, 0 < ε n) (hlim : Tendsto ε atTop (𝓝 0)) (x : H) :
    Tendsto (fun n => supportResolvent B (ε n) x) atTop (𝓝 (rangeSupport B x)) := by
…

    Mentions: OAI.KadisonSimilarity.supportResolvent, OAI.KadisonSimilarity.rangeSupport