Theorems · Theorem · functional analysis
CFC.norm_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.norm_nnrpow._auto_1 → ‖a ^ r‖ = ‖a‖ ^ ↑r- Cited by
- 0 results in Mathlib
- Foundations
- Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites15
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 · cited by 5,413
- 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 and proof · cited by 1,260
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointstatement and proof · cited by 545
- NonnegSpectrumClassstatement and proof · cited by 292
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