Theorems · Theorem · operator theory

ContinuousLinearMap.IsPositive.adjoint_conj

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedAddCommGroup F] [inst_3 : InnerProductSpace 𝕜 E] [inst_4 : InnerProductSpace 𝕜 F]
  [inst_5 : CompleteSpace E] [inst_6 : CompleteSpace F] {T : E →L[𝕜] E},
  T.IsPositive → ∀ (S : F →L[𝕜] E), (ContinuousLinearMap.adjoint S ∘SL T ∘SL S).IsPositive

Defined in

Mathlib.Analysis.InnerProductSpace.Positive

Cited by

1 results in Mathlib

Foundations

Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupNormedAddCommGroupInnerProductSpaceInnerProductSpaceCompleteSpaceCompleteSpace