Theorems · Definition · functional analysis

Submodule.linearProjOfClosedCompl

Deprecated since 2026-06-07Use Submodule.projectionOntoL instead.

{𝕜 : Type u_1} →
  {E : Type u_2} →
    [inst : NontriviallyNormedField 𝕜] →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] →
          [CompleteSpace E] → (p q : Subspace 𝕜 E) → IsCompl p q → IsClosed ↑p → IsClosed ↑q → E →L[𝕜] ↥p

Projection to a closed submodule along a closed complement.

Defined in

Mathlib.Analysis.Normed.Module.Complemented

Cited by

2 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceCompleteSpace