Theorems · Definition · functional analysis
TensorProduct.lidIsometry
(𝕜 : Type u_1) →
(E : Type u_2) →
[inst : RCLike 𝕜] →
[inst_1 : NormedAddCommGroup E] → [inst_2 : InnerProductSpace 𝕜 E] → TensorProduct 𝕜 𝕜 E ≃ₗᵢ[𝕜] EThe linear isometry equivalence version of TensorProduct.lid.
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 245 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- TensorProductstatement · cited by 2,545
- LinearIsometryEquivstatement · cited by 748
- TensorProduct.lidproof · cited by 96
- LinearEquiv.isometryOfInnerproof · cited by 3
- TensorProduct.inner_lid_lidproof · cited by 1
Cited by10
Results whose statement or proof uses this declaration.
- TensorProduct.toLinearEquiv_lidIsometrystatement · cited by 0
- TensorProduct.nnnorm_lidproof · cited by 0
- TensorProduct.norm_lidproof · cited by 0
- TensorProduct.commIsometry_trans_lidIsometrystatement · cited by 0
- TensorProduct.commIsometry_trans_ridIsometrystatement · cited by 0
- TensorProduct.toContinuousLinearMap_symm_lidIsometrystatement · cited by 0
- TensorProduct.enorm_lidproof · cited by 0
- TensorProduct.lidIsometry_applystatement · cited by 0
- TensorProduct.lidIsometry_eq_ridIsometrystatement · cited by 0
- TensorProduct.lidIsometry_symm_applystatement · cited by 0