Theorems · Definition · functional analysis

DoubleCentralizer.toProdMulOpposite

{𝕜 : Type u_1} →
  {A : Type u_2} →
    [inst : NontriviallyNormedField 𝕜] →
      [inst_1 : NonUnitalNormedRing A] →
        [inst_2 : NormedSpace 𝕜 A] →
          [inst_3 : SMulCommClass 𝕜 A A] →
            [inst_4 : IsScalarTower 𝕜 A A] → DoubleCentralizer 𝕜 A → (A →L[𝕜] A) × (A →L[𝕜] A)ᵐᵒᵖ

The natural injection from DoubleCentralizer.toProd except the second coordinate inherits MulOpposite.op. The ring structure on 𝓜(𝕜, A) is the pullback under this map.

Defined in

Mathlib.Analysis.CStarAlgebra.Multiplier

Cited by

4 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNonUnitalNormedRingNormedSpaceSMulCommClassIsScalarTower