Theorems · Theorem · functional analysis
isStarProjection_iff_mem_extremePoints_setOfPred_nonneg_inter_unitClosedBall
∀ {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)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
- 1 results in Mathlib
- Foundations
- Depth 323 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Moduleproof · cited by 20,661
- Semiringproof · cited by 13,802
- PartialOrderstatement and proof · cited by 6,410
- Set.ofPredstatement and proof · cited by 6,101
- Complexproof · cited by 5,565
- Norm.normproof · cited by 5,413
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
Cited by1
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- isStarProjection_iff_mem_extremePoints_setOf_nonneg_inter_unitClosedBallproof · cited by 0