feat(QM): unbounded operator inequalities#993
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gloges wants to merge 8 commits intoleanprover-community:masterfrom
Open
feat(QM): unbounded operator inequalities#993gloges wants to merge 8 commits intoleanprover-community:masterfrom
gloges wants to merge 8 commits intoleanprover-community:masterfrom
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t-quantum-mechanics |
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RFC |
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| ring_nf | ||
| rw [Complex.I_sq] | ||
| ring |
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Would grind [Complex.I_sq] work here?
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Thanks, that worked a charm!
| simp only [inner_conj_symm] | ||
| refine ⟨fun hT x ↦ (hT x x).symm, ?_⟩ | ||
| intro h x y | ||
| rw [inner_map_polarization, inner_map_polarization'] |
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| rw [inner_map_polarization, inner_map_polarization'] | |
| refine ⟨fun hT x ↦ (hT x x).symm, fun h x y ↦ ?_⟩ |
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| · intro u v huv | ||
| refine (adjoint_apply_eq U₁.dense_domain v ?_).symm | ||
| exact fun x ↦ huv ▸ heq x u |
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| · intro u v huv | |
| refine (adjoint_apply_eq U₁.dense_domain v ?_).symm | |
| exact fun x ↦ huv ▸ heq x u | |
| · exact fun u v huv => (adjoint_apply_eq U₁.dense_domain v (fun x ↦ huv ▸ heq x u).symm |
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Thanks, I have made the suggested changes. |
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| refine ⟨?_, fun h ↦ h ▸ closure_isClosed U⟩ | ||
| intro h |
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| refine ⟨?_, fun h ↦ h ▸ closure_isClosed U⟩ | |
| intro h | |
| refine ⟨fun h ↦ ?_, fun h ↦ h ▸ closure_isClosed U⟩ |
| lemma isSelfAdjoint_isClosed {T : UnboundedOperator H H} (hT : IsSelfAdjoint T) : IsClosed T := | ||
| hT ▸ adjoint_isClosed T | ||
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| lemma isSelfAdjoint_isSymmetric {T : UnboundedOperator H H} (hT : IsSelfAdjoint T) : |
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isSymmetric_of_isSelfAdjoint probably a better name here
| SetLike.val_smul, inner_smul_left, Complex.conj_I, inner_smul_right] | ||
| grind [Complex.I_sq] | ||
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| lemma inner_map_polarization' (x y : T.domain) : |
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This lemma and the one above might be better suited further up the file
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IsSymmetricfor unbounded operators and shows this is equivalent to having⟪Tx, x⟫real.le_adjoint_adjoint,adjoint_ge_adjoint_of_leandclosure_mono).isSymmetric_iff_le_adjoint).(cf. #982 for poset)