Theorems · Theorem · functional analysis
ContinuousLinearMap.opNNNorm_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‖₊ ≤ 1- Defined in
- Mathlib.Analysis.Normed.Operator.Mul
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- ContinuousLinearMapstatement · cited by 5,352
- NNRealstatement · cited by 4,310
- IsScalarTowerstatement and proof · cited by 3,896
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NormedAlgebrastatement and proof · cited by 1,165
- NNNorm.nnnormstatement · cited by 952
- SeminormedRingstatement and proof · cited by 446
- IsBoundedSMulstatement and proof · cited by 329
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.opENorm_lsmul_leproof · cited by 2