Theorems · Theorem · functional analysis
CFC.posPart_sub_negPart
∀ {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] (a : A),
autoParam (IsSelfAdjoint a) CFC.posPart_sub_negPart._auto_1 → a⁺ - a⁻ = a- Cited by
- 10 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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
- CommSemiringproof · cited by 10,911
- IsScalarTowerstatement and proof · cited by 3,896
- Nontrivialproof · cited by 2,416
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- MetricSpaceproof · cited by 1,684
- IsSelfAdjointstatement and proof · cited by 545
- ContinuousStarproof · cited by 543
- neg_zeroproof · cited by 542
Cited by10
Results whose statement or proof uses this declaration.
- CStarAlgebra.linear_combination_nonnegproof · cited by 2
- CFC.negPart_eq_zero_iffproof · cited by 1
- CFC.negPart_eq_of_eq_PosPart_subproof · cited by 1
- spectrum_star_mul_self_nonnegproof · cited by 1
- CFC.le_posPartproof · cited by 0
- CFC.neg_negPart_leproof · cited by 0
- CFC.posPart_eq_of_eq_sub_negPartproof · cited by 0
- CFC.abs_sub_selfproof · cited by 0
- CFC.posPart_eq_zero_iffproof · cited by 0
- CFC.abs_add_selfproof · cited by 0