Theorems · Inductive type · functional analysis
MulAlgebraNorm
(R : Type u_1) → [inst : SeminormedCommRing R] → (S : Type u_2) → [inst_1 : Ring S] → [Algebra R S] → Type u_2
A multiplicative algebra norm on an R-algebra norm S is a multiplicative ring norm on S
compatible with the action of R.
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement · cited by 11,388
- Ringstatement · cited by 7,463
- SeminormedCommRingstatement · cited by 38
Cited by26
Results whose statement or proof uses this declaration.
- spectralMulAlgNormstatement · cited by 5
- MulAlgebraNorm.toMulRingNormstatement and proof · cited by 4
- NormedAlgebra.toMulAlgebraNormstatement · cited by 2
- spectralNorm.spectralMulAlgNorm_eq_of_mem_rootsstatement · cited by 1
- spectralNorm.spectralNorm_pow_natDegree_eq_prod_rootsstatement · cited by 1
- MulAlgebraNorm.coe_AlgebraNormstatement and proof · cited by 1
- MulAlgebraNorm.extstatement and proof · cited by 1
- MulAlgebraNorm.extends_norm'statement and proof · cited by 1
- MulAlgebraNorm.mk.injstatement · cited by 1
- MulAlgebraNorm.smul'statement and proof · cited by 1
- MulAlgebraNorm.toAlgebraNormstatement and proof · cited by 1
- MulAlgebraNorm.toFun_eq_coestatement and proof · cited by 1