Theorems · Theorem · functional analysis
CFC.abs_algebraMap
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : RCLike 𝕜] [inst_1 : Ring A] [inst_2 : TopologicalSpace A] [inst_3 : StarRing A]
[inst_4 : PartialOrder A] [inst_5 : StarOrderedRing A] [inst_6 : Algebra 𝕜 A] [inst_7 : Algebra ℝ A]
[inst_8 : NonnegSpectrumClass ℝ A] [IsTopologicalRing A] [T2Space A]
[inst_11 : ContinuousFunctionalCalculus ℝ A IsSelfAdjoint] [StarModule 𝕜 A] [StarModule ℝ A] [IsScalarTower ℝ 𝕜 A]
(c : 𝕜), CFC.abs ((algebraMap 𝕜 A) c) = (algebraMap ℝ A) ‖c‖- Cited by
- 0 results in Mathlib
- Foundations
- Depth 217 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- PartialOrderstatement and proof · cited by 6,410
- Norm.normstatement and proof · cited by 5,413
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- RCLikestatement and proof · cited by 2,829
- StarRingstatement and proof · cited by 1,686
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