Theorems · Theorem · functional analysis
CFC.norm_star_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 (0 ≤ a) CFC.norm_star_mul_mul_self_of_nonneg._auto_1 → ‖star b * a * b‖ = ‖CFC.sqrt a * b‖ ^ 2- Cited by
- 3 results in Mathlib
- Foundations
- Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- mul_assocproof · cited by 1,667
- Star.starstatement and proof · cited by 1,082
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointstatement and proof · cited by 545
- NonnegSpectrumClassstatement and proof · cited by 292
Cited by3
Results whose statement or proof uses this declaration.
- CFC.norm_mul_mul_star_self_of_nonnegproof · cited by 1
- IsStarProjection.mul_right_and_mul_left_of_nonneg_of_leproof · cited by 1
- CFC.IsSelfAdjoint.norm_mul_mul_self_of_nonnegproof · cited by 0