| import Mathlib.Analysis.VonNeumannAlgebra.Basic | |
| namespace OAI | |
| open scoped Pointwise | |
| namespace Invariant233 | |
| variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] | |
| [CompleteSpace H] | |
| local instance instStarModuleGenerated : StarModule ℂ (H →L[ℂ] H) := | |
| ContinuousLinearMap.instStarModuleId | |
| noncomputable def vonNeumannGenerated (s : Set (H →L[ℂ] H)) : VonNeumannAlgebra H where | |
| toStarSubalgebra := | |
| StarSubalgebra.centralizer ℂ (StarSubalgebra.centralizer ℂ s : Set (H →L[ℂ] H)) | |
| centralizer_centralizer' := by | |
| change Set.centralizer (Set.centralizer | |
| (StarSubalgebra.centralizer ℂ (StarSubalgebra.centralizer ℂ s : Set (H →L[ℂ] H)) : | |
| Set (H →L[ℂ] H))) = _ | |
| rw [StarSubalgebra.coe_centralizer_centralizer] | |
| rw [Set.centralizer_centralizer_centralizer] | |
| exact (StarSubalgebra.coe_centralizer_centralizer ℂ s).symm | |
| end Invariant233 | |
| end OAI | |