Theorems · Definition · functional analysis

ContinuousLinearMap.ofIsClosedGraph

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_3} →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] →
          [CompleteSpace E] →
            {F : Type u_5} →
              [inst_4 : NormedAddCommGroup F] →
                [inst_5 : NormedSpace 𝕜 F] → [CompleteSpace F] → {g : E →ₗ[𝕜] F} → IsClosed ↑g.graph → E →L[𝕜] F

Upgrade a LinearMap to a ContinuousLinearMap using the closed graph theorem.

Defined in

Mathlib.Analysis.Normed.Operator.Banach

Cited by

2 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceCompleteSpaceNormedAddCommGroupNormedSpaceCompleteSpace