Theorems · Definition · functional analysis

LinearIsometry.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] → (F →ₗᵢ[𝕜] G) → TensorProduct 𝕜 E F →ₗᵢ[𝕜] TensorProduct 𝕜 E G

This is the natural linear isometry induced by f : F ≃ₗᵢ G.

Defined in

Mathlib.Analysis.InnerProductSpace.TensorProduct

Cited by

5 results in Mathlib

Foundations

Depth 245 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpaceNormedAddCommGroupInnerProductSpace