Theorems · Theorem · functional analysis
ContinuousLinearMap.mem_invtSubmodule_adjoint_iff
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
[inst_3 : CompleteSpace E] {T : E →L[𝕜] E} {U : Submodule 𝕜 E} [U.HasOrthogonalProjection],
U ∈ Module.End.invtSubmodule ↑(ContinuousLinearMap.adjoint T) ↔ Uᗮ ∈ Module.End.invtSubmodule ↑T- Cited by
- 1 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.
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 and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement and proof · cited by 7,192
- ContinuousLinearMapstatement and proof · 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.toLinearMapstatement and proof · cited by 528
- Submodule.orthogonalstatement and proof · cited by 257
Cited by1
Results whose statement or proof uses this declaration.
- Module.End.mem_invtSubmodule_adjoint_iffproof · cited by 0