toCompletelyPositiveLinearMap — Mathlib

English

Non-unital star algebra homomorphisms are completely positive maps.

Русский

Ненулевой звездной гомоморфизм образует полностью положительный отображатель.

LaTeX

$$NonUnitalStarAlgHomClass F Complex A₁ A₂ ⇒ CompletelyPositiveMapClass F A₁ A₂$$

Lean4

/-- Reinterpret an element of a type of completely positive maps as a completely positive linear
  map. -/
@[coe]
def toCompletelyPositiveLinearMap [CompletelyPositiveMapClass F A₁ A₂] (f : F) : A₁ →CP A₂ :=
  { (f : A₁ →ₗ[ℂ] A₂) with map_cstarMatrix_nonneg' := CompletelyPositiveMapClass.map_cstarMatrix_nonneg' f }

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