Theorems · Theorem · functional analysis
CFC.IsSelfAdjoint.norm_mul_mul_self_of_nonneg
∀ {A : Type u_1} [inst : PartialOrder A] [inst_1 : NonUnitalNormedRing A] [inst_2 : StarRing A] [CStarRing A]
[inst_4 : NormedSpace ℝ A] [inst_5 : SMulCommClass ℝ A A] [inst_6 : IsScalarTower ℝ A A] [inst_7 : StarOrderedRing A]
[inst_8 : NonUnitalContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [inst_9 : NonnegSpectrumClass ℝ A] {a : A} (b : A),
autoParam (IsSelfAdjoint b) CFC.IsSelfAdjoint.norm_mul_mul_self_of_nonneg._auto_1 →
autoParam (0 ≤ a) CFC.IsSelfAdjoint.norm_mul_mul_self_of_nonneg._auto_3 → ‖b * a * b‖ = ‖CFC.sqrt a * b‖ ^ 2- Cited by
- 0 results in Mathlib
- Foundations
- Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- NormedSpacestatement and proof · cited by 12,499
- PartialOrderstatement and proof · cited by 6,410
- Norm.normstatement and proof · cited by 5,413
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointstatement and proof · cited by 545
- NonnegSpectrumClassstatement and proof · cited by 292
- NonUnitalContinuousFunctionalCalculusstatement and proof · cited by 275
- NonUnitalNormedRingstatement and proof · cited by 231
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.