Theorems · Inductive type · functional analysis

DoubleCentralizer

(𝕜 : Type u) →
  (A : Type v) →
    [inst : NontriviallyNormedField 𝕜] →
      [inst_1 : NonUnitalNormedRing A] →
        [inst_2 : NormedSpace 𝕜 A] → [SMulCommClass 𝕜 A A] → [IsScalarTower 𝕜 A A] → Type v

The type of double centralizers, also known as the multiplier algebra and denoted by 𝓜(𝕜, A), of a non-unital normed algebra. If x : 𝓜(𝕜, A), then x.fst and x.snd are what is usually referred to as $L$ and $R$.

Defined in

Mathlib.Analysis.CStarAlgebra.Multiplier

Cited by

59 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNonUnitalNormedRingNormedSpaceSMulCommClassIsScalarTower