Theorems · Theorem · functional analysis
VonNeumannAlgebra.mem_commutant_iff
∀ {H : Type u} [inst : NormedAddCommGroup H] [inst_1 : InnerProductSpace ℂ H] [inst_2 : CompleteSpace H]
{S : VonNeumannAlgebra H} {z : H →L[ℂ] H}, z ∈ S.commutant ↔ ∀ g ∈ S, g * z = z * g- Defined in
- Mathlib.Analysis.VonNeumannAlgebra.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
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- Setproof · cited by 53,352
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Complexstatement and proof · cited by 5,565
- ContinuousLinearMapstatement and proof · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- CompleteSpacestatement and proof · cited by 2,532
- SetLike.mem_coeproof · cited by 302
- VonNeumannAlgebrastatement and proof · cited by 16
- VonNeumannAlgebra.commutantstatement · cited by 5
- VonNeumannAlgebra.coe_commutantproof · cited by 2
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