feat(QuantumMechanics): Add LinearPMap.compRestricted#1127
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| adjoint_isFormalAdjoint h₁ ⟨u, u.2.1⟩ ⟨w, w.2.1⟩, | ||
| adjoint_isFormalAdjoint h₂ ⟨u, u.2.2⟩ ⟨w, w.2.2⟩] | ||
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| lemma adjoint_comp_le_comp_adjoint [CompleteSpace H] [CompleteSpace H'] |
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should this be compRestricted not comp in the name?
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Thanks, I've fixed this and three other lemma names.
jstoobysmith
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May 27, 2026
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Looks good to me. Will merge once linters finish
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The composition of two partial linear maps,
g.comp f, requires a proof that the range offis contained in the domain ofg. This PR definesg.compRestricted f(g ∘ᵣ f) which automatically restricts the domain offto thosexfor whichg (f x)is defined.Also includes:
g ∘ᵣ fand the relationship betweeng ∘ᵣ fand other compositions ofgwithf.U† ∘ᵣ V† ≤ (V ∘ᵣ U)†. (The same inequality but with∘ᵣreplaced by any composition on either side follows immediately from this,comp_le_compRestrictedandadjoint_antitone.)Tis symmetric then so too isT ∘ᵣ T.𝓜 f ∘ᵣ 𝓜 g ≤ 𝓜 (f • g)with equality when𝓜 gis bounded.