Theorems · Theorem · functional analysis

ContinuousLinearMap.IsStarProjection.ext_iff

∀ {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} [inst_3 : CompleteSpace E] {S : E →L[𝕜] E},
  IsStarProjection S → IsStarProjection T → (S = T ↔ (↑S).range = (↑T).range)

Star projection operators are equal iff their range are.

Defined in

Mathlib.Analysis.InnerProductSpace.Adjoint

Cited by

2 results in Mathlib

Foundations

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

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceCompleteSpace