Theorems · Theorem · functional analysis
CStarAlgebra.linear_combination_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] [inst_6 : StarModule ℂ A]
[inst_7 : NonUnitalContinuousFunctionalCalculus ℝ A IsSelfAdjoint] (x : A),
(↑(realPart x))⁺ - (↑(realPart x))⁻ + (Complex.I • (↑(imaginaryPart x))⁺ - Complex.I • (↑(imaginaryPart x))⁻) = x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · 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
- RingHom.idstatement · cited by 18,349
- LinearMapstatement · cited by 10,215
- Complexstatement and proof · cited by 5,565
- IsScalarTowerstatement and proof · cited by 3,896
- AddSubgroupstatement · cited by 3,232
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- Complex.Istatement and proof · cited by 866
Cited by2
Results whose statement or proof uses this declaration.
- CStarAlgebra.exists_sum_four_nonnegproof · cited by 1
- CStarAlgebra.span_nonnegproof · cited by 1