Theorems · Theorem · functional analysis
VonNeumannAlgebra.coe_commutant
∀ {H : Type u} [inst : NormedAddCommGroup H] [inst_1 : InnerProductSpace ℂ H] [inst_2 : CompleteSpace H]
(S : VonNeumannAlgebra H), ↑S.commutant = (↑S).centralizer- Defined in
- Mathlib.Analysis.VonNeumannAlgebra.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- SetLike.coestatement and proof · cited by 8,199
- Complexstatement and proof · cited by 5,565
- ContinuousLinearMapstatement · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- CompleteSpacestatement and proof · cited by 2,532
- Set.centralizerstatement and proof · cited by 57
- Set.union_selfproof · cited by 32
- VonNeumannAlgebrastatement and proof · cited by 16
- StarMemClass.star_coe_eqproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- VonNeumannAlgebra.commutant_commutantproof · cited by 1
- VonNeumannAlgebra.mem_commutant_iffproof · cited by 0