Theorems · Theorem · functional analysis
CFC.posPart_mul_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), a⁺ * a⁻ = 0- Cited by
- 0 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites32
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
- MulZeroClass.mul_zeroproof · cited by 2,091
- 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
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