Theorems · Theorem · functional analysis
isStarProjection_iff_mem_extremePoints_setOf_nonneg_inter_unitClosedBall
Deprecated since 2026-07-09Use isStarProjection_iff_mem_extremePoints_setOfPred_nonneg_inter_unitClosedBall instead.
∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {e : A},
IsStarProjection e ↔ e ∈ Set.extremePoints ℝ ({x | 0 ≤ x} ∩ Metric.closedBall 0 1)Alias of isStarProjection_iff_mem_extremePoints_setOfPred_nonneg_inter_unitClosedBall.
The star projections in a non-unital C⋆-algebra are exactly the extreme points of
the nonnegative closed unit ball.
- Defined in
- Mathlib.Analysis.CStarAlgebra.Extreme
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 324 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement · cited by 25,697
- PartialOrderstatement · cited by 6,410
- Set.ofPredstatement · cited by 6,101
- Metric.closedBallstatement · cited by 704
- StarOrderedRingstatement · cited by 587
- NonUnitalCStarAlgebrastatement · cited by 149
- IsStarProjectionstatement · cited by 64
- Set.extremePointsstatement · cited by 43
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