Theorems · Theorem · functional analysis
LinearIsometry.norm_toContinuousLinearMap
∀ {𝕜 : Type u_1} {𝕜₂ : Type u_3} {E : Type u_5} {F : Type u_6} [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} [NontrivialTopology E] [RingHomIsometric σ₁₂]
(f : E →ₛₗᵢ[σ₁₂] F), ‖f.toContinuousLinearMap‖ = 1- Cited by
- 13 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.
Cites14
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
- RingHomIsometricstatement and proof · cited by 282
- LinearIsometrystatement and proof · cited by 194
- LinearIsometry.toContinuousLinearMapstatement and proof · cited by 47
- NontrivialTopologystatement and proof · cited by 46
Cited by13
Results whose statement or proof uses this declaration.
- Complex.ofRealCLM_normproof · cited by 2
- Complex.conjCLE_normproof · cited by 2
- LinearIsometry.nnnorm_toContinuousLinearMapproof · cited by 2
- ContinuousLinearMap.opNorm_mulproof · cited by 1
- RCLike.conjCLE_normproof · cited by 0
- ContinuousLinearMap.norm_inlproof · cited by 0
- ContinuousLinearMap.norm_inrproof · cited by 0
- InnerProductSpace.innerSL_normproof · cited by 0
- LinearIsometryEquiv.norm_toContinuousLinearMapproof · cited by 0
- UniformSpace.Completion.norm_toComplLproof · cited by 0
- ContinuousLinearMap.norm_singleproof · cited by 0
- RCLike.ofRealCLM_normproof · cited by 0