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revert some changes
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jcommelin committed Oct 8, 2024
1 parent 944b2aa commit ec84c9b
Showing 1 changed file with 9 additions and 9 deletions.
Original file line number Diff line number Diff line change
Expand Up @@ -649,14 +649,14 @@ variable {A : Type*} [TopologicalSpace A] [Ring A] [PartialOrder A] [StarRing A]

lemma cfcHom_nnreal_eq_restrict {a : A} (ha : 0 ≤ a) :
cfcHom ha = (SpectrumRestricts.nnreal_of_nonneg ha).starAlgHom
(cfcHom (IsSelfAdjoint.of_nonneg ha)) :=
(SpectrumRestricts.nnreal_of_nonneg ha).cfcHom_eq_restrict _ isUniformEmbedding_subtype_val _ _
(cfcHom (IsSelfAdjoint.of_nonneg ha)) := by
apply (SpectrumRestricts.nnreal_of_nonneg ha).cfcHom_eq_restrict _ isUniformEmbedding_subtype_val

lemma cfc_nnreal_eq_real {a : A} (f : ℝ≥0 → ℝ≥0) (ha : 0 ≤ a := by cfc_tac) :
cfc f a = cfc (fun x ↦ f x.toNNReal : ℝ → ℝ) a := by
replace ha : 0 ≤ a := ha -- hack to avoid issues caused by autoParam
exact (SpectrumRestricts.nnreal_of_nonneg ha).cfc_eq_restrict _
isUniformEmbedding_subtype_val ha (.of_nonneg ha) _
apply (SpectrumRestricts.nnreal_of_nonneg ha).cfc_eq_restrict _
isUniformEmbedding_subtype_val ha (.of_nonneg ha)

end NNRealEqReal

Expand All @@ -673,15 +673,15 @@ variable {A : Type*} [TopologicalSpace A] [NonUnitalRing A] [PartialOrder A] [St

lemma cfcₙHom_nnreal_eq_restrict {a : A} (ha : 0 ≤ a) :
cfcₙHom ha = (QuasispectrumRestricts.nnreal_of_nonneg ha).nonUnitalStarAlgHom
(cfcₙHom (IsSelfAdjoint.of_nonneg ha)) :=
(QuasispectrumRestricts.nnreal_of_nonneg ha).cfcₙHom_eq_restrict _
isUniformEmbedding_subtype_val _ _
(cfcₙHom (IsSelfAdjoint.of_nonneg ha)) := by
apply (QuasispectrumRestricts.nnreal_of_nonneg ha).cfcₙHom_eq_restrict _
isUniformEmbedding_subtype_val

lemma cfcₙ_nnreal_eq_real {a : A} (f : ℝ≥0 → ℝ≥0) (ha : 0 ≤ a := by cfc_tac) :
cfcₙ f a = cfcₙ (fun x ↦ f x.toNNReal : ℝ → ℝ) a := by
replace ha : 0 ≤ a := ha -- hack to avoid issues caused by autoParam
exact (QuasispectrumRestricts.nnreal_of_nonneg ha).cfcₙ_eq_restrict _
isUniformEmbedding_subtype_val ha (.of_nonneg ha) _
apply (QuasispectrumRestricts.nnreal_of_nonneg ha).cfcₙ_eq_restrict _
isUniformEmbedding_subtype_val ha (.of_nonneg ha)

end NNRealEqRealNonUnital

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