Theorems · Theorem · functional analysis
ContinuousLinearMap.le_opNNNorm
∀ {𝕜 : Type u_1} {𝕜₂ : Type u_2} {E : Type u_4} {F : Type u_5} [inst : NontriviallyNormedField 𝕜]
[inst_1 : NontriviallyNormedField 𝕜₂] [inst_2 : SeminormedAddCommGroup E] [inst_3 : SeminormedAddCommGroup F]
[inst_4 : NormedSpace 𝕜 E] [inst_5 : NormedSpace 𝕜₂ F] {σ₁₂ : 𝕜 →+* 𝕜₂} [inst_6 : RingHomIsometric σ₁₂]
(f : E →SL[σ₁₂] F) (x : E), ‖f x‖₊ ≤ ‖f‖₊ * ‖x‖₊- Defined in
- Mathlib.Analysis.Normed.Operator.NNNorm
- Cited by
- 6 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.
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
- NormedSpacestatement and proof · cited by 12,499
- RingHomstatement and proof · cited by 10,189
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement and proof · cited by 5,352
- NNRealstatement · cited by 4,310
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NNNorm.nnnormstatement · cited by 952
- RingHomIsometricstatement and proof · cited by 282
- ContinuousLinearMap.le_opNormproof · cited by 65
Cited by6
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.lipschitzproof · cited by 16
- ContinuousLinearMap.le_opENormproof · cited by 11
- DoubleCentralizer.norm_fst_eq_sndproof · cited by 3
- Module.Basis.opNNNorm_leproof · cited by 2
- MeasureTheory.eLpNorm_le_eLpNorm_fderiv_of_eqproof · cited by 1
- MeasureTheory.VectorMeasure.variation_transpose_eq_smulproof · cited by 1