Theorems · Theorem · commutative algebra
spectralNorm_eq_invariantExtension
∀ (K : Type u_2) [inst : NormedField K] (L : Type u_3) [inst_1 : Field L] [inst_2 : Algebra K L] [h_fin : FiniteDimensional K L] [hn : Normal K L] [hu : IsUltrametricDist K], spectralNorm K L = ⇑(IsUltrametricDist.invariantExtension K L)
If L/K is finite and normal, then spectralNorm K L = invariantExtension K L.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Norm.normproof · cited by 5,413
- Algebra.algebraMapproof · cited by 4,706
- iSupproof · cited by 2,415
- FiniteDimensionalstatement and proof · cited by 1,854
- AlgEquivproof · cited by 1,681
- NormedFieldstatement and proof · cited by 1,084
- IsUltrametricDiststatement and proof · cited by 177
- Normalstatement and proof · cited by 92
Cited by3
Results whose statement or proof uses this declaration.
- isNonarchimedean_spectralNorm_of_finiteDimensional_normalproof · cited by 1
- isPowMul_spectralNorm_of_finiteDimensional_normalproof · cited by 1
- spectralNorm_extends_of_finiteDimensionalproof · cited by 0