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fix merge
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j-loreaux committed Oct 28, 2024
1 parent 67c1a06 commit 3942ef4
Showing 1 changed file with 3 additions and 3 deletions.
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Expand Up @@ -180,16 +180,16 @@ instance IsStarNormal.instNonUnitalContinuousFunctionalCalculus {A : Type*}
[NonUnitalCStarAlgebra A] : NonUnitalContinuousFunctionalCalculus ℂ (IsStarNormal : A → Prop) :=
RCLike.nonUnitalContinuousFunctionalCalculus Unitization.isStarNormal_inr

open Unitization in
open Unitization CStarAlgebra in
lemma inr_comp_cfcₙHom_eq_cfcₙAux {A : Type*} [NonUnitalCStarAlgebra A] (a : A)
[ha : IsStarNormal a] : (inrNonUnitalStarAlgHom ℂ A).comp (cfcₙHom ha) =
cfcₙAux (isStarNormal_inr (R := ℂ) (A := A)) a ha := by
have h (a : A) := isStarNormal_inr (R := ℂ) (A := A) (a := a)
refine @UniqueNonUnitalContinuousFunctionalCalculus.eq_of_continuous_of_map_id
_ _ _ _ _ _ _ _ _ _ _ inferInstance inferInstance _ (σₙ ℂ a) _ _ rfl _ _ ?_ ?_ ?_
· show Continuous (fun f ↦ (cfcₙHom ha f : Unitization ℂ A)); fun_prop
· show Continuous (fun f ↦ (cfcₙHom ha f : A⁺¹)); fun_prop
· exact isClosedEmbedding_cfcₙAux @(h) a ha |>.continuous
· trans (a : Unitization ℂ A)
· trans (a : A⁺¹)
· congrm(inr $(cfcₙHom_id ha))
· exact cfcₙAux_id @(h) a ha |>.symm

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