Theorems · Theorem · commutative algebra
spectralNorm_eq_of_equiv
∀ {K : Type u_2} [inst : NormedField K] {L : Type u_3} [inst_1 : Field L] [inst_2 : Algebra K L] (σ : Gal(L/K)) (x : L),
spectralNorm K L x = spectralNorm K L (σ x)The K-algebra automorphisms of L are isometries with respect to the spectral norm.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedFieldFieldAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement · cited by 25,697
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- AlgEquivstatement and proof · cited by 1,681
- NormedFieldstatement and proof · cited by 1,084
- minpolyproof · cited by 439
- spectralNormstatement · cited by 31
- spectralValueproof · cited by 13
- minpoly.algEquiv_eqproof · cited by 13
Cited by1
Results whose statement or proof uses this declaration.
- IsKrasner.of_completeSpace_of_normalproof · cited by 0