Theorems · Theorem · operator theory

Submodule.starProjection_le_starProjection_iff

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {U V : Submodule 𝕜 E} [inst_3 : U.HasOrthogonalProjection] [inst_4 : V.HasOrthogonalProjection],
  U.starProjection ≤ V.starProjection ↔ U ≤ V

U.starProjection ≤ V.starProjection iff U ≤ V.

Defined in

Mathlib.Analysis.InnerProductSpace.Positive

Cited by

0 results in Mathlib

Foundations

Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceSubmodule.HasOrthogonalProjectionSubmodule.HasOrthogonalProjection