Theorems · Theorem · functional analysis
ContinuousLinearMap.adjoint_id
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
[inst_3 : CompleteSpace E], ContinuousLinearMap.adjoint (ContinuousLinearMap.id 𝕜 E) = ContinuousLinearMap.id 𝕜 E- Cited by
- 0 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- ContinuousLinearMapstatement · cited by 5,352
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- CompleteSpacestatement and proof · cited by 2,532
- LinearIsometryEquivstatement · cited by 748
- starRingEndstatement · cited by 671
- ContinuousLinearMap.idstatement and proof · cited by 233
- ContinuousLinearMap.adjointstatement · cited by 82
- LinearMap.IsSymmetric.clm_adjoint_eqproof · cited by 8
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