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9eeb9c7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | 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
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