Theorems · Theorem · functional analysis
ContinuousLinearMap.rTensor_eq_mapL
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} (G : Type u_4) [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : InnerProductSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : InnerProductSpace 𝕜 F]
[inst_5 : NormedAddCommGroup G] [inst_6 : InnerProductSpace 𝕜 G] (f : E →L[𝕜] F),
ContinuousLinearMap.rTensor G f = TensorProduct.mapL f (ContinuousLinearMap.id 𝕜 G)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 266 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.
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- ContinuousLinearMapstatement and proof · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- TensorProductstatement and proof · cited by 2,545
- ContinuousLinearMap.idstatement and proof · cited by 233
- ContinuousLinearMap.comp.congr_simpproof · cited by 77
- ContinuousLinearMap.rTensorstatement and proof · cited by 32
- ContinuousLinearMap.lTensorproof · cited by 30
- TensorProduct.mapLstatement · cited by 27
- ContinuousLinearMap.comp_idproof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.adjoint_rTensorproof · cited by 0