Theorems · Theorem · functional analysis
norm_algebraMap
∀ {𝕜 : Type u_1} (𝕜' : Type u_2) [inst : NormedField 𝕜] [inst_1 : SeminormedRing 𝕜'] [inst_2 : NormedAlgebra 𝕜 𝕜']
(x : 𝕜), ‖(algebraMap 𝕜 𝕜') x‖ = ‖x‖ * ‖1‖- Defined in
- Mathlib.Analysis.Normed.Module.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
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
- RingHomstatement · cited by 10,189
- Norm.normstatement and proof · cited by 5,413
- Algebra.algebraMapstatement · cited by 4,706
- NormedAlgebrastatement and proof · cited by 1,165
- NormedFieldstatement and proof · cited by 1,084
- SeminormedRingstatement and proof · cited by 446
- norm_smulproof · cited by 242
- Algebra.algebraMap_eq_smul_oneproof · cited by 119
Cited by5
Results whose statement or proof uses this declaration.
- norm_algebraMap'proof · cited by 39
- spectrum.mem_resolventSet_of_norm_lt_mulproof · cited by 3
- nnnorm_algebraMapproof · cited by 1
- NormedAlgebra.Complex.exists_norm_sub_smul_one_eq_zeroproof · cited by 0
- dist_algebraMapproof · cited by 0