Theorems · Theorem · functional analysis
ContinuousLinearMap.opNNNorm_lsmul_apply_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] (x : R),
‖(ContinuousLinearMap.lsmul 𝕜 R) x‖₊ ≤ ‖x‖₊- Defined in
- Mathlib.Analysis.Normed.Operator.Mul
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- 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 and proof · cited by 952
- SeminormedRingstatement and proof · cited by 446
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