Theorems · Theorem · functional analysis
CFC.nnrpow_def
∀ {A : Type u_1} [inst : PartialOrder A] [inst_1 : NonUnitalRing A] [inst_2 : TopologicalSpace A] [inst_3 : StarRing A]
[inst_4 : Module ℝ A] [inst_5 : SMulCommClass ℝ A A] [inst_6 : IsScalarTower ℝ A A] [inst_7 : StarOrderedRing A]
[inst_8 : NonUnitalContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [inst_9 : NonnegSpectrumClass ℝ A] {a : A}
{y : NNReal}, a ^ y = cfcₙ (fun x => x.nnrpow y) a- Cited by
- 3 results in Mathlib
- Foundations
- Depth 201 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
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- 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
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointstatement and proof · cited by 545
- NonUnitalRingstatement and proof · cited by 422
- NonnegSpectrumClassstatement and proof · cited by 292
Cited by3
Results whose statement or proof uses this declaration.
- CFC.nnrpow_eq_rpowproof · cited by 6
- CFC.nnrpow_eq_cfcₙ_realproof · cited by 1
- CFC.exists_measure_nnrpow_eq_integral_cfcₙ_rpowIntegrand₁₂proof · cited by 0