Theorems · Theorem · functional analysis
ContinuousLinearMap.opNorm_lsmul_le
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : SeminormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {R : Type u_3} [inst_3 : SeminormedRing R] [inst_4 : NormedAlgebra 𝕜 R]
[inst_5 : Module R E] [inst_6 : IsBoundedSMul R E] [inst_7 : IsScalarTower 𝕜 R E], ‖ContinuousLinearMap.lsmul 𝕜 R‖ ≤ 1The norm of lsmul is at most 1 in any semi-normed group.
- Defined in
- Mathlib.Analysis.Normed.Operator.Mul
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normstatement · cited by 5,413
- ContinuousLinearMapstatement · cited by 5,352
- IsScalarTowerstatement and proof · cited by 3,896
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NormedAlgebrastatement and proof · cited by 1,165
- SeminormedRingstatement and proof · cited by 446
- IsBoundedSMulstatement and proof · cited by 329
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.dist_convolution_leproof · cited by 2
- ContinuousLinearMap.opNNNorm_lsmul_leproof · cited by 1
- norm_iteratedFDerivWithin_smul_leproof · cited by 0
- norm_iteratedFDeriv_smul_leproof · cited by 0