| import Mathlib | |
| import OAI.Analysis.Commutator.DerivationBoundTransfer | |
| import OAI.Analysis.Commutator.StableUniversalAssembly | |
| namespace OAI | |
| noncomputable section | |
| section | |
| noncomputable section | |
| namespace Kadison | |
| variable {A H : Type*} [CStarAlgebra A] [NormedAddCommGroup H] | |
| [InnerProductSpace ℂ H] [CompleteSpace H] | |
| local instance : PartialOrder A := CStarAlgebra.spectralOrder A | |
| local instance : StarOrderedRing A := CStarAlgebra.spectralOrderedRing A | |
| theorem all_bounded_derivations_inner (σ : A →⋆ₐ[ℂ] (H →L[ℂ] H)) | |
| (D : A →L[ℂ] (H →L[ℂ] H)) | |
| (hD : ∀ a b,D (a*b)=(D a).comp (σ b)+(σ a).comp (D b)) : | |
| ∃ V : H →L[ℂ] H,‖V‖≤(1+9368)^2*‖D‖ ∧ | |
| ∀ a : A,D a=V.comp (σ a)-(σ a).comp V := by | |
| exact DerivationColumns.implementation_of_bicommutant_bound σ D hD (by norm_num : (0:ℝ)≤9368) | |
| (fun Y h hh X hX => CentralSpectral.universal_bound _ Y h hh X hX) | |
| end Kadison | |
| end | |
| end | |
| end | |
| end OAI | |