Theorems · Theorem · functional analysis
CFC.nnnorm_rpow
∀ {A : Type u_1} [inst : NormedRing A] [inst_1 : StarRing A] [inst_2 : NormedAlgebra ℝ A] [inst_3 : PartialOrder A]
[inst_4 : StarOrderedRing A] [inst_5 : NonnegSpectrumClass ℝ A]
[inst_6 : IsometricContinuousFunctionalCalculus ℝ A IsSelfAdjoint] (a : A) {r : ℝ},
0 < r → autoParam (0 ≤ a) CFC.nnnorm_rpow._auto_1 → ‖a ^ r‖₊ = ‖a‖₊ ^ r- Cited by
- 1 results in Mathlib
- Foundations
- Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- PartialOrderstatement and proof · cited by 6,410
- NNRealstatement and proof · cited by 4,310
- LT.lt.leproof · cited by 2,189
- StarRingstatement and proof · cited by 1,686
- NNReal.toRealproof · cited by 1,260
- NormedAlgebrastatement and proof · cited by 1,165
- NNNorm.nnnormstatement and proof · cited by 952
- NormedRingstatement and proof · cited by 924
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointstatement and proof · cited by 545
- NonnegSpectrumClassstatement and proof · cited by 292
Cited by1
Results whose statement or proof uses this declaration.
- CFC.norm_rpowproof · cited by 0