Theorems · Theorem · operator theory
LinearPMap.mem_adjoint_domain_iff
∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
[inst_2 : InnerProductSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : InnerProductSpace 𝕜 F] (T : E →ₗ.[𝕜] F)
[inst_5 : CompleteSpace E] (y : F), y ∈ T.adjoint.domain ↔ Continuous ⇑((innerₛₗ 𝕜) y ∘ₗ T.toFun)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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 and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- LinearMapstatement · cited by 10,215
- Submodulestatement · cited by 7,192
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- Continuousstatement · cited by 2,592
- CompleteSpacestatement and proof · cited by 2,532
- LinearMap.compstatement · cited by 1,642
- starRingEndstatement · cited by 671
- LinearPMapstatement and proof · cited by 179
Cited by2
Results whose statement or proof uses this declaration.
- LinearPMap.mem_adjoint_domain_of_existsproof · cited by 2
- IsSelfAdjoint.dense_domainproof · cited by 1