Theorems · Definition · functional analysis

ContinuousLinearMap.lTensor

{𝕜 : Type u_1} →
  {E : Type u_2} →
    {F : Type u_3} →
      (G : Type u_4) →
        [inst : RCLike 𝕜] →
          [inst_1 : NormedAddCommGroup E] →
            [inst_2 : InnerProductSpace 𝕜 E] →
              [inst_3 : NormedAddCommGroup F] →
                [inst_4 : InnerProductSpace 𝕜 F] →
                  [inst_5 : NormedAddCommGroup G] →
                    [inst_6 : InnerProductSpace 𝕜 G] → (E →L[𝕜] F) → TensorProduct 𝕜 G E →L[𝕜] TensorProduct 𝕜 G F

LinearMap.lTensor as a continuous linear map, i.e. the continuous linear map g extended to the map x ⊗ₜ[𝕜] y ↦ x ⊗ₜ[𝕜] g(y).

Defined in

Mathlib.Analysis.InnerProductSpace.TensorProduct

Cited by

30 results in Mathlib

Foundations

Depth 263 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpace