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feat(CStarAlgebra): log is operator concave#38540

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dupuisf:concaveOn_log
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feat(CStarAlgebra): log is operator concave#38540
dupuisf wants to merge 1 commit intoleanprover-community:masterfrom
dupuisf:concaveOn_log

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@dupuisf dupuisf commented Apr 26, 2026

This PR shows that the log is operator concave, i.e. CFC.log is concave on strictly positive elements of a unital C⋆-algebra.


The proof has a lot in common with the proof that the log is operator monotone; I tried to extract the common elements as well as I could, hence the rather ugly-looking auxiliary lemmas. (One of them is private to avoid making more imports public.)

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@dupuisf dupuisf added the t-analysis Analysis (normed *, calculus) label Apr 26, 2026
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PR summary 2113b17760

Import changes for modified files

Dependency changes

File Base Count Head Count Change
Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Order 2759 2760 +1 (+0.04%)
Import changes for all files
Files Import difference
Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Order 1

Declarations diff

+ CFC.cfc_rpow_sub_one_eqOn
+ CFC.concaveOn_log
+ CFC.tendsto_ite_cfc_rpow_sub_one_ite_log

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.


No changes to technical debt.

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/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).

@dupuisf dupuisf requested a review from j-loreaux April 26, 2026 02:50
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