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feat(Analysis/CStarAlgebra): set of star projections equals the extreme points of the nonnegative closed unit ball#36201

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feat(Analysis/CStarAlgebra): set of star projections equals the extreme points of the nonnegative closed unit ball#36201
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@themathqueen themathqueen commented Mar 5, 2026

An element in a non-unital C⋆-algebra is a projection iff it is an extreme point of the nonnegative closed unit ball. This is from 1.6.2 in Sakai's C⋆-algebras and W⋆-algebras (the proof is different though).

Co-authored-by: Jon Bannon [email protected]


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github-actions bot commented Mar 5, 2026

PR summary 82ff5788d3

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.Analysis.CStarAlgebra.Extreme (new file) 2679

Declarations diff

+ isStarProjection_iff_mem_extremePoints_nonneg_inter_unitClosedBall

You can run this locally as follows
## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.


Increase in tech debt: (relative, absolute) = (1.00, 0.00)
Current number Change Type
10161 1 backward.isDefEq

Current commit 1a09c5d1e9
Reference commit 82ff5788d3

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./scripts/reporting/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@github-actions github-actions bot added the t-analysis Analysis (normed *, calculus) label Mar 5, 2026
@mathlib-dependent-issues mathlib-dependent-issues bot added the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Mar 5, 2026
@mathlib-dependent-issues mathlib-dependent-issues bot removed the blocked-by-other-PR This PR depends on another PR (this label is automatically managed by a bot) label Mar 11, 2026
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@j-loreaux j-loreaux added the awaiting-author A reviewer has asked the author a question or requested changes. label Mar 12, 2026
@themathqueen themathqueen removed the awaiting-author A reviewer has asked the author a question or requested changes. label Mar 13, 2026
@j-loreaux j-loreaux removed their assignment Mar 18, 2026
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I've removed my assignment since my name is listed as one of the authors of the new file.

@mathlib-triage mathlib-triage bot assigned loefflerd and unassigned ADedecker Mar 31, 2026
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I'm afraid I don't know enough about the area to meaningfully review this. In my opinion, if @j-loreaux , @themathqueen and @JonBannon are happy with each others' contributions, then that is convincing enough.

@loefflerd loefflerd removed their assignment Apr 1, 2026
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