Theorems · Theorem · functional analysis
ContinuousLinearMap.opNorm_mul_flip_apply
∀ (𝕜 : Type u_1) {E : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NonUnitalNormedRing E]
[inst_2 : StarRing E] [NormedStarGroup E] [inst_4 : NormedSpace 𝕜 E] [inst_5 : IsScalarTower 𝕜 E E]
[inst_6 : SMulCommClass 𝕜 E E] [RegularNormedAlgebra 𝕜 E] (a : E), ‖(ContinuousLinearMap.mul 𝕜 E).flip a‖ = ‖a‖- Cited by
- 2 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- 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 and proof · cited by 5,413
- ContinuousLinearMapstatement · cited by 5,352
- IsScalarTowerstatement and proof · cited by 3,896
- mul_commproof · cited by 2,262
- le_antisymmproof · cited by 2,068
- SMulCommClassstatement and proof · cited by 1,927
- StarRingstatement and proof · cited by 1,686
Cited by2
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.opNNNorm_mul_flip_applyproof · cited by 0
- ContinuousLinearMap.isometry_mul_flipproof · cited by 0