Theorems · Definition · commutative algebra
spectralMulAlgNorm
(K : Type u) →
[inst : NontriviallyNormedField K] →
(L : Type v) →
[inst_1 : Field L] →
[inst_2 : Algebra K L] →
[Algebra.IsAlgebraic K L] → [hu : IsUltrametricDist K] → [CompleteSpace K] → MulAlgebraNorm K LThe spectral norm is a multiplicative K-algebra norm on L.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 230 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Fieldstatement and proof · cited by 7,404
- CompleteSpacestatement and proof · cited by 2,532
- Algebra.IsAlgebraicstatement and proof · cited by 322
- IsUltrametricDiststatement and proof · cited by 177
- AlgebraNormproof · cited by 39
- RingSeminorm.toAddGroupSeminormproof · cited by 16
- MulAlgebraNormstatement · cited by 15
- RingNorm.toRingSeminormproof · cited by 11
- spectralAlgNormproof · cited by 9
- AlgebraNorm.toRingNormproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- spectralNorm.spectralMulAlgNorm_eq_of_mem_rootsstatement · cited by 1
- spectralNorm.spectralNorm_pow_natDegree_eq_prod_rootsstatement and proof · cited by 1
- spectralMulAlgNorm_defstatement · cited by 1
- spectralMulAlgNorm.congr_simpstatement and proof · cited by 0
- spectralNorm.spectralNorm_eq_norm_coeff_zero_rpowproof · cited by 0