Theorems · Theorem · functional analysis
CStarAlgebra.norm_negPart_le
∀ {A : Type u_1} [inst : NonUnitalNormedRing A] [inst_1 : NormedSpace ℝ A] [inst_2 : SMulCommClass ℝ A A]
[inst_3 : IsScalarTower ℝ A A] [inst_4 : StarRing A]
[inst_5 : NonUnitalIsometricContinuousFunctionalCalculus ℝ A IsSelfAdjoint] (a : A), ‖a⁻‖ ≤ ‖a‖- Cited by
- 2 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- 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
- IsSelfAdjointstatement and proof · cited by 545
- NonUnitalNormedRingstatement and proof · cited by 231
- norm_negproof · cited by 190
- NegPart.negPartstatement · cited by 107
- NonUnitalIsometricContinuousFunctionalCalculusstatement and proof · cited by 68
- CFC.posPart_negproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- CStarAlgebra.exists_sum_four_nonnegproof · cited by 1
- IsSelfAdjoint.norm_eq_max_norm_posPart_negPartproof · cited by 0