Theorems · Theorem · functional analysis
CFC.nnnorm_nnrpow
∀ {A : Type u_1} [inst : NonUnitalNormedRing A] [inst_1 : StarRing A] [inst_2 : NormedSpace ℝ A]
[inst_3 : IsScalarTower ℝ A A] [inst_4 : SMulCommClass ℝ A A] [inst_5 : PartialOrder A] [inst_6 : StarOrderedRing A]
[inst_7 : NonnegSpectrumClass ℝ A] [inst_8 : NonUnitalIsometricContinuousFunctionalCalculus ℝ A IsSelfAdjoint] (a : A)
{r : NNReal}, 0 < r → autoParam (0 ≤ a) CFC.nnnorm_nnrpow._auto_1 → ‖a ^ r‖₊ = ‖a‖₊ ^ ↑r- Cited by
- 3 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- NNRealstatement and proof · cited by 4,310
- IsScalarTowerstatement and proof · cited by 3,896
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
- NNReal.toRealstatement · cited by 1,260
- NNNorm.nnnormstatement · cited by 952
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointstatement and proof · cited by 545
- quasispectrumproof · cited by 292
Cited by3
Results whose statement or proof uses this declaration.
- CFC.nnnorm_rpowproof · cited by 1
- CFC.nnnorm_sqrtproof · cited by 1
- CFC.norm_nnrpowproof · cited by 0