Theorems · Theorem · operator theory

LinearPMap.IsFormalAdjoint.symm

∀ {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}
  {S : F →ₗ.[𝕜] E}, T.IsFormalAdjoint S → S.IsFormalAdjoint T

Defined in: Mathlib.Analysis.InnerProductSpace.LinearPMap
Cited by: 2 results in Mathlib
Foundations: Depth 47 from the axioms · uses propext, Quot.sound
Assumes: RCLike NormedAddCommGroup InnerProductSpace NormedAddCommGroup InnerProductSpace

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Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
RingHom.idstatement and proof · 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
Inner.innerproof · cited by 1,089
starRingEndproof · cited by 671
LinearPMapstatement and proof · cited by 179
LinearPMap.domainproof · cited by 167
LinearPMap.toFun'proof · cited by 124
inner_conj_symmproof · cited by 48
LinearPMap.IsFormalAdjointstatement and proof · cited by 3

Cited by2

Results whose statement or proof uses this declaration.

LinearPMap.adjoint_graph_eq_graph_adjointproof · cited by 2
LinearPMap.IsFormalAdjoint.le_adjointproof · cited by 0