Theorems · Theorem · functional analysis
CStarAlgebra.norm_posPart_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
- 3 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- Moduleproof · cited by 20,661
- NormedSpacestatement and proof · cited by 12,499
- CommSemiringproof · cited by 10,911
- Norm.normstatement and proof · cited by 5,413
- IsScalarTowerstatement and proof · cited by 3,896
- Nontrivialproof · cited by 2,416
- LT.lt.leproof · cited by 2,189
- 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
Cited by3
Results whose statement or proof uses this declaration.
- CStarAlgebra.norm_negPart_leproof · cited by 2
- CStarAlgebra.exists_sum_four_nonnegproof · cited by 1
- IsSelfAdjoint.norm_eq_max_norm_posPart_negPartproof · cited by 0