VonNeumannAlgebra pMp for projection p#45
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VonNeumannAlgebra pMp for projection p#45themathqueen wants to merge 2 commits intoj-loreaux:masterfrom
VonNeumannAlgebra pMp for projection p#45themathqueen wants to merge 2 commits intoj-loreaux:masterfrom
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themathqueen
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VonNeumannAlgebra p.range for projection pVonNeumannAlgebra pMp for projection p
j-loreaux
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Jan 22, 2026
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| @[simp] theorem IsStarProjection.starProjection_range_eq {p : H →L[ℂ] H} (hp : IsStarProjection p) | ||
| [p.range.HasOrthogonalProjection] : p.range.starProjection = p := |
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The assumption p.range.HasOrthogonalProjection is redundant since p.range is closed.
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| abbrev VonNeumannAlgebra.IsStarProjection.range {p : H →L[ℂ] H} (hp : IsStarProjection p) | ||
| (hpM : p ∈ M) : | ||
| letI : CompleteSpace p.range := hp.isIdempotentElem.isClosed_range.completeSpace_coe | ||
| VonNeumannAlgebra p.range := by |
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I think we'll actually want to create a subtype for projections first. There are naturally reasons to do so (e.g., they have a CompleteLattice structure). Then you will only cut down a von Neumann algebra by an element of the subtype.
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