Theorems · Theorem · functional analysis
CFC.posPart_smul_of_nonneg
∀ {A : Type u_1} [inst : NonUnitalRing A] [inst_1 : Module ℝ A] [inst_2 : SMulCommClass ℝ A A]
[inst_3 : IsScalarTower ℝ A A] [inst_4 : StarRing A] [inst_5 : TopologicalSpace A]
[inst_6 : NonUnitalContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [T2Space A] [StarModule ℝ A] {r : ℝ},
0 ≤ r → ∀ {a : A}, (r • a)⁺ = r • a⁺- Cited by
- 2 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- T2Spacestatement and proof · cited by 1,351
- StarModulestatement and proof · cited by 570
- IsSelfAdjointstatement and proof · cited by 545
- NonUnitalRingstatement and proof · cited by 422
- NonUnitalContinuousFunctionalCalculusstatement and proof · cited by 275
- PosPart.posPartstatement · cited by 113
Cited by2
Results whose statement or proof uses this declaration.
- CFC.posPart_smul_of_nonposproof · cited by 1
- CFC.negPart_smul_of_nonposproof · cited by 0