Theorems · Theorem · functional analysis
CFC.rpow_neg_one_eq_cfc_inv
∀ {A : Type u_2} [inst : PartialOrder A] [inst_1 : NormedRing A] [inst_2 : StarRing A] [inst_3 : StarOrderedRing A]
[inst_4 : NormedAlgebra ℝ A] [inst_5 : NonnegSpectrumClass ℝ A]
[inst_6 : ContinuousFunctionalCalculus ℝ A IsSelfAdjoint] (a : A), a ^ (-1) = cfc (fun x => x⁻¹) a- Cited by
- 1 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- StarRingstatement and proof · cited by 1,686
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- StarOrderedRingstatement and proof · cited by 587
- IsSelfAdjointstatement and proof · cited by 545
- spectrumproof · cited by 510
- ContinuousFunctionalCalculusstatement and proof · cited by 331
- NonnegSpectrumClassstatement and proof · cited by 292
- cfcstatement · cited by 228
Cited by1
Results whose statement or proof uses this declaration.
- CFC.monotoneOn_one_sub_one_add_invproof · cited by 2