Theorems · Theorem · functional analysis
AlgebraNorm.extends_norm
∀ {R : Type u_1} [inst : SeminormedCommRing R] {S : Type u_2} [inst_1 : Ring S] [inst_2 : Algebra R S]
{f : AlgebraNorm R S}, f 1 = 1 → ∀ (a : R), f ((algebraMap R S) a) = ‖a‖An R-algebra norm such that f 1 = 1 extends the norm on R.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 · cited by 25,697
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Norm.normstatement and proof · cited by 5,413
- Algebra.algebraMapstatement · cited by 4,706
- Algebra.algebraMap_eq_smul_oneproof · cited by 119
- AlgebraNormstatement and proof · cited by 39
- SeminormedCommRingstatement and proof · cited by 38
- AlgebraNorm.extends_norm'proof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- max_norm_root_eq_spectralValueproof · cited by 1