Theorems · Theorem · functional analysis
CStarAlgebra.span_nonneg
∀ {A : Type u_1} [inst : NonUnitalRing A] [inst_1 : Module ℂ A] [inst_2 : SMulCommClass ℂ A A]
[inst_3 : IsScalarTower ℂ A A] [inst_4 : StarRing A] [inst_5 : TopologicalSpace A] [StarModule ℂ A]
[NonUnitalContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [inst_8 : PartialOrder A] [StarOrderedRing A],
Submodule.span ℂ {a | 0 ≤ a} = ⊤A C⋆-algebra is spanned by its nonnegative elements.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- Top.topstatement and proof · cited by 9,680
- Submodulestatement · 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
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
Cited by1
Results whose statement or proof uses this declaration.
- CStarAlgebra.span_nonneg_inter_closedBallproof · cited by 2