Theorems · Definition · functional analysis

DoubleCentralizer.coe

(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] → A → DoubleCentralizer 𝕜 A

The natural coercion of A into 𝓜(𝕜, A) given by sending a : A to the pair of linear maps Lₐ Rₐ : A →L[𝕜] A given by left- and right-multiplication by a, respectively. Warning: if A = 𝕜, then this is a coercion which is not definitionally equal to the algebraMap 𝕜 𝓜(𝕜, 𝕜) coercion, but these are propositionally equal. See DoubleCentralizer.coe_eq_algebraMap below.

Defined in

Mathlib.Analysis.CStarAlgebra.Multiplier

Cited by

4 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNonUnitalNormedRingNormedSpaceSMulCommClassIsScalarTower