| import Mathlib | |
| import OAI.Analysis.Commutator.BiprodLinkColumn | |
| namespace OAI | |
| noncomputable section | |
| section | |
| noncomputable section | |
| namespace Kadison.BiprodLinkColumn | |
| open HilbertBiprod PartialIsometryOrder | |
| variable {H G : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] | |
| [NormedAddCommGroup G] [InnerProductSpace ℂ G] [CompleteSpace G] | |
| variable (N : VonNeumannAlgebra (Space H G)) (S : Set (Intertwiner N)) | |
| lemma compression_empty : compression N S ∅=0 := by | |
| simp only [compression,finiteProjection,Finset.sum_empty,ContinuousLinearMap.zero_comp, | |
| ContinuousLinearMap.comp_zero] | |
| end Kadison.BiprodLinkColumn | |
| end | |
| end | |
| end | |
| end OAI | |