Theorems · Theorem · functional analysis
ContinuousLinearMap.adjoint_innerSL_apply
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
[inst_3 : CompleteSpace E] (x : E),
ContinuousLinearMap.adjoint ((innerSL 𝕜) x) = ContinuousLinearMap.toSpanSingleton 𝕜 x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- 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
- one_mulproof · cited by 2,841
- RCLikestatement and proof · cited by 2,829
- CompleteSpacestatement and proof · cited by 2,532
- one_smulproof · cited by 1,374
- Inner.innerproof · cited by 1,089
- LinearIsometryEquivstatement · cited by 748
- starRingEndstatement · cited by 671
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.adjoint_innerₛₗ_applyproof · cited by 0