Theorems · Theorem · operator theory

ContinuousLinearMap.IsPositive.orthogonalProjectionOnto_comp

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {T : E →L[𝕜] E},
  T.IsPositive →
    ∀ (U : Submodule 𝕜 E) [inst_3 : U.HasOrthogonalProjection],
      (U.orthogonalProjectionOnto ∘SL T ∘SL U.subtypeL).IsPositive

Defined in

Mathlib.Analysis.InnerProductSpace.Positive

Cited by

1 results in Mathlib

Foundations

Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceSubmodule.HasOrthogonalProjection