Theorems · Theorem · functional analysis
LinearIsometry.norm_toContinuousLinearMap_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} (f : E →ₛₗᵢ[σ₁₂] F),
‖f.toContinuousLinearMap‖ ≤ 1- Defined in
- Mathlib.Analysis.Normed.Operator.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- RingHomstatement and proof · cited by 10,189
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement and proof · cited by 5,413
- ContinuousLinearMapstatement · cited by 5,352
- one_mulproof · cited by 2,841
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- zero_le_oneproof · cited by 316
- LinearIsometrystatement and proof · cited by 194
- ContinuousLinearMap.opNorm_le_boundproof · cited by 59
- LinearIsometry.toContinuousLinearMapstatement and proof · cited by 47
Cited by5
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.norm_lTensor_leproof · cited by 1
- Submodule.norm_subtypeL_leproof · cited by 0
- ContinuousLinearMap.norm_inl_le_oneproof · cited by 0
- ContinuousLinearMap.norm_inr_le_oneproof · cited by 0
- ContinuousLinearMap.norm_single_le_oneproof · cited by 0