Theorems · Theorem · functional analysis
ContinuousLinearMap.le_opNorm_of_le
∀ {𝕜 : Type u_1} {𝕜₂ : Type u_2} {E : Type u_4} {F : Type u_5} [inst : SeminormedAddCommGroup E]
[inst_1 : SeminormedAddCommGroup F] [inst_2 : NontriviallyNormedField 𝕜] [inst_3 : NontriviallyNormedField 𝕜₂]
[inst_4 : NormedSpace 𝕜 E] [inst_5 : NormedSpace 𝕜₂ F] {σ₁₂ : 𝕜 →+* 𝕜₂} [RingHomIsometric σ₁₂] (f : E →SL[σ₁₂] F)
{c : ℝ} {x : E}, ‖x‖ ≤ c → ‖f x‖ ≤ ‖f‖ * c- Defined in
- Mathlib.Analysis.Normed.Operator.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 166 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- RingHomstatement and proof · cited by 10,189
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement and proof · cited by 5,413
- ContinuousLinearMapstatement and proof · cited by 5,352
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- le_rflproof · cited by 1,558
- RingHomIsometricstatement and proof · cited by 282
- ContinuousLinearMap.le_of_opNorm_le_of_leproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.opNorm_comp_leproof · cited by 16
- ContinuousLinearMap.norm_compContinuousMultilinearMap_leproof · cited by 6
- ContinuousLinearMap.unit_le_opNormproof · cited by 4
- ContinuousLinearMap.sSup_unit_ball_eq_nnnormproof · cited by 2
- ContinuousLinearMap.sSup_sphere_eq_nnnormproof · cited by 1