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chore: fix merge failure
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jcommelin committed Oct 8, 2024
1 parent 6f1861d commit 2470147
Showing 1 changed file with 6 additions and 6 deletions.
Original file line number Diff line number Diff line change
Expand Up @@ -605,7 +605,7 @@ variable {A : Type*} [TopologicalSpace A] [Ring A] [StarRing A] [Algebra ℂ A]

lemma cfcHom_real_eq_restrict {a : A} (ha : IsSelfAdjoint a) :
cfcHom ha = ha.spectrumRestricts.starAlgHom (cfcHom ha.isStarNormal) (f := Complex.reCLM) :=
ha.spectrumRestricts.cfcHom_eq_restrict _ Complex.isometry_ofReal.uniformEmbedding
ha.spectrumRestricts.cfcHom_eq_restrict _ Complex.isometry_ofReal.isUniformEmbedding
ha ha.isStarNormal

lemma cfc_real_eq_complex {a : A} (f : ℝ → ℝ) (ha : IsSelfAdjoint a := by cfc_tac) :
Expand All @@ -626,7 +626,7 @@ variable {A : Type*} [TopologicalSpace A] [NonUnitalRing A] [StarRing A] [Module
lemma cfcₙHom_real_eq_restrict {a : A} (ha : IsSelfAdjoint a) :
cfcₙHom ha = (ha.quasispectrumRestricts.2).nonUnitalStarAlgHom (cfcₙHom ha.isStarNormal)
(f := Complex.reCLM) :=
ha.quasispectrumRestricts.2.cfcₙHom_eq_restrict _ Complex.isometry_ofReal.uniformEmbedding
ha.quasispectrumRestricts.2.cfcₙHom_eq_restrict _ Complex.isometry_ofReal.isUniformEmbedding
ha ha.isStarNormal

lemma cfcₙ_real_eq_complex {a : A} (f : ℝ → ℝ) (ha : IsSelfAdjoint a := by cfc_tac) :
Expand All @@ -650,13 +650,13 @@ 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 _ uniformEmbedding_subtype_val _ _
(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 _
uniformEmbedding_subtype_val ha (.of_nonneg ha) _
isUniformEmbedding_subtype_val ha (.of_nonneg ha) _

end NNRealEqReal

Expand All @@ -675,13 +675,13 @@ 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 _
uniformEmbedding_subtype_val _ _
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 _
uniformEmbedding_subtype_val ha (.of_nonneg ha) _
isUniformEmbedding_subtype_val ha (.of_nonneg ha) _

end NNRealEqRealNonUnital

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