Theorems · Theorem · functional analysis
ContinuousMultilinearMap.norm_mkPiRing
∀ {𝕜 : Type u} {ι : Type v} {G : Type wG} [inst : NontriviallyNormedField 𝕜] [inst_1 : SeminormedAddCommGroup G]
[inst_2 : NormedSpace 𝕜 G] [inst_3 : Fintype ι] (z : G), ‖ContinuousMultilinearMap.mkPiRing 𝕜 ι z‖ = ‖z‖- Cited by
- 4 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · 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 and proof · cited by 5,413
- one_mulproof · cited by 2,841
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- ContinuousMultilinearMapstatement and proof · cited by 1,016
- ContinuousMultilinearMap.mkPiAlgebraproof · cited by 13
- ContinuousMultilinearMap.mkPiRingstatement · cited by 11
- ContinuousMultilinearMap.norm_mkPiAlgebraproof · cited by 2
- ContinuousMultilinearMap.norm_smulRightproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- ContinuousMultilinearMap.piFieldEquivproof · cited by 15
- FormalMultilinearSeries.norm_apply_eq_norm_coefproof · cited by 3
- norm_cauchyPowerSeries_leproof · cited by 1
- spectrum.hasFPowerSeriesOnBall_inverse_one_sub_smulproof · cited by 1
- spectrum.limsup_pow_nnnorm_pow_one_div_le_spectralRadiusproof · cited by 1