Theorems · Theorem · functional analysis
VonNeumannAlgebra.commutant_commutant
∀ {H : Type u} [inst : NormedAddCommGroup H] [inst_1 : InnerProductSpace ℂ H] [inst_2 : CompleteSpace H]
(S : VonNeumannAlgebra H), S.commutant.commutant = S- Defined in
- Mathlib.Analysis.VonNeumannAlgebra.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NormedAddCommGroupstatement and proof · cited by 15,752
- SetLike.coeproof · cited by 8,199
- Complexstatement and proof · cited by 5,565
- InnerProductSpacestatement and proof · cited by 3,523
- CompleteSpacestatement and proof · cited by 2,532
- SetLike.coe_injectiveproof · cited by 374
- Set.centralizerproof · cited by 57
- VonNeumannAlgebrastatement and proof · cited by 16
- VonNeumannAlgebra.commutantstatement and proof · cited by 5
- VonNeumannAlgebra.coe_commutantproof · cited by 2
- VonNeumannAlgebra.centralizer_centralizerproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- VonNeumannAlgebra.IsIdempotentElem.mem_iffproof · cited by 1