Theorems · Theorem · functional analysis
CStarAlgebra.span_nonneg_inter_ball
∀ {A : Type u_1} [inst : NonUnitalCStarAlgebra A] [inst_1 : PartialOrder A] [StarOrderedRing A] {r : ℝ},
0 < r → Submodule.span ℂ ({x | 0 ≤ x} ∩ Metric.ball 0 r) = ⊤A C⋆-algebra is spanned by nonnegative elements of norm less than r.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 315 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- 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
- le_reflproof · cited by 2,061
- Submodule.spanstatement and proof · cited by 1,504
- Metric.ballstatement and proof · cited by 735
- StarOrderedRingstatement and proof · cited by 587
- eq_top_iffproof · cited by 236
Cited by1
Results whose statement or proof uses this declaration.
- CStarAlgebra.span_nonneg_inter_unitBallproof · cited by 1