Theorems · Definition · functional analysis

InnerProductSpace.continuousLinearMapOfBilin

{𝕜 : Type u_1} →
  {E : Type u_2} →
    [inst : RCLike 𝕜] →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : InnerProductSpace 𝕜 E] → [CompleteSpace E] → (E →L⋆[𝕜] E →L[𝕜] 𝕜) → E →L[𝕜] E

Maps a bounded sesquilinear form to its continuous linear map, given by interpreting the form as a map B : E →L⋆[𝕜] StrongDual 𝕜 E and dualizing the result using toDual.

Defined in

Mathlib.Analysis.InnerProductSpace.Dual

Cited by

10 results in Mathlib

Foundations

Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceCompleteSpace