Theorems · Theorem · functional analysis
ContinuousMultilinearMap.norm_smulRight
∀ {𝕜 : Type u} {ι : Type v} {E : ι → Type wE} {G : Type wG} [inst : NontriviallyNormedField 𝕜]
[inst_1 : (i : ι) → SeminormedAddCommGroup (E i)] [inst_2 : (i : ι) → NormedSpace 𝕜 (E i)]
[inst_3 : SeminormedAddCommGroup G] [inst_4 : NormedSpace 𝕜 G] [inst_5 : Fintype ι]
(f : ContinuousMultilinearMap 𝕜 E 𝕜) (z : G), ‖f.smulRight z‖ = ‖f‖ * ‖z‖- Cited by
- 1 results in Mathlib
- Foundations
- Depth 171 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.
- Realstatement · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Fintypestatement and proof · cited by 7,736
- Norm.normstatement · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NNReal.toRealproof · cited by 1,260
- ContinuousMultilinearMapstatement and proof · cited by 1,016
- ContinuousMultilinearMap.smulRightstatement · cited by 10
- ContinuousMultilinearMap.nnnorm_smulRightproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousMultilinearMap.norm_mkPiRingproof · cited by 4