Theorems · Theorem · functional analysis
CStarAlgebra.span_nonneg_inter_closedBall
∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {r : ℝ},
0 < r → Submodule.span ℂ ({x | 0 ≤ x} ∩ Metric.closedBall 0 r) = ⊤A C⋆-algebra is spanned by nonnegative elements of norm at most r
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 314 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Top.topstatement · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- PartialOrderstatement and proof · cited by 6,410
- Set.ofPredstatement and proof · cited by 6,101
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- mul_oneproof · cited by 3,885
- Nat.cast_zeroproof · cited by 1,870
- Complex.ofRealproof · cited by 1,654
Cited by2
Results whose statement or proof uses this declaration.
- CStarAlgebra.span_nonneg_inter_ballproof · cited by 1
- CStarAlgebra.span_nonneg_inter_unitClosedBallproof · cited by 0