Theorems · Theorem · functional analysis
ContinuousLinearMap.opNorm_mul_le
∀ (𝕜 : Type u_1) [inst : NontriviallyNormedField 𝕜] (R : Type u_3) [inst_1 : NonUnitalSeminormedRing R] [inst_2 : NormedSpace 𝕜 R] [inst_3 : IsScalarTower 𝕜 R R] [inst_4 : SMulCommClass 𝕜 R R], ‖ContinuousLinearMap.mul 𝕜 R‖ ≤ 1
- Defined in
- Mathlib.Analysis.Normed.Operator.Mul
- Cited by
- 1 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- 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
- SMulCommClassstatement and proof · cited by 1,927
- zero_le_oneproof · cited by 316
- ContinuousLinearMap.mulstatement · cited by 63
- LinearMap.mulproof · cited by 61
- NonUnitalSeminormedRingstatement and proof · cited by 44
Cited by1
Results whose statement or proof uses this declaration.
- norm_iteratedFDerivWithin_mul_leproof · cited by 2