Theorems · Theorem · functional analysis
ContinuousMultilinearMap.nnnorm_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 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Fintypestatement and proof · cited by 7,736
- NNRealstatement and proof · cited by 4,310
- Finset.univproof · cited by 3,473
- LE.le.transproof · cited by 3,151
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Finset.prodproof · cited by 2,356
- MulZeroClass.mul_zeroproof · cited by 2,091
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousMultilinearMap.norm_smulRightproof · cited by 1