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feat(QuantumMechanics): Add orthogonal subspaces#1208

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jstoobysmith merged 6 commits into
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gloges:orthog-subspaces
Jun 19, 2026
Merged

feat(QuantumMechanics): Add orthogonal subspaces#1208
jstoobysmith merged 6 commits into
leanprover-community:masterfrom
gloges:orthog-subspaces

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@gloges

@gloges gloges commented Jun 19, 2026

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Adds several orthogonal subspaces for unbounded operators:

  • HasDenseDomain.orthogonal_range : U.rangeᗮ = U†.ker
  • HasDenseDomain.orthogonal_adjoint_ker : U†.kerᗮ = U.range.closure
  • IsUnbounded.orthogonal_adjoint_range : U†.rangeᗮ = U.closure.ker
  • IsUnbounded.orthogonal_closure_ker : U.closure.kerᗮ = U†.range

Also two variants useful for the spectral theory (the latter holds for z in the regularity domain):

  • IsUnbounded.orthogonal_closure_sub_range : (T.closure - z • 1).rangeᗮ = (T† - conj z • 1).ker
  • IsUnbounded.orthogonal_adjoint_sub_ker : (T† - conj z • 1).kerᗮ = (T.closure - z • 1).range

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gloges commented Jun 19, 2026

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t-quantum-mechanics

@github-actions github-actions Bot added the t-quantum-mechanics Quantum mechanics label Jun 19, 2026
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Thank you for this PR, which will now be reviewed.
If submitting to ./Physlib or ./QuantumInfo, please
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@jstoobysmith jstoobysmith left a comment

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This all looks good to me! Approved. Many thanks.

@jstoobysmith jstoobysmith added the ready-to-merge This PR is approved and will be merged shortly label Jun 19, 2026
@jstoobysmith jstoobysmith merged commit bd681b2 into leanprover-community:master Jun 19, 2026
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ready-to-merge This PR is approved and will be merged shortly t-quantum-mechanics Quantum mechanics

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