Theorems · Definition · functional analysis

ContinuousLinearMap.precompR

{𝕜 : Type u_1} →
  {E : Type u_4} →
    (Eₗ : Type u_5) →
      {Fₗ : Type u_7} →
        {Gₗ : Type u_9} →
          [inst : SeminormedAddCommGroup E] →
            [inst_1 : SeminormedAddCommGroup Eₗ] →
              [inst_2 : SeminormedAddCommGroup Fₗ] →
                [inst_3 : SeminormedAddCommGroup Gₗ] →
                  [inst_4 : NontriviallyNormedField 𝕜] →
                    [inst_5 : NormedSpace 𝕜 E] →
                      [inst_6 : NormedSpace 𝕜 Eₗ] →
                        [inst_7 : NormedSpace 𝕜 Fₗ] →
                          [inst_8 : NormedSpace 𝕜 Gₗ] → (E →L[𝕜] Fₗ →L[𝕜] Gₗ) → E →L[𝕜] (Eₗ →L[𝕜] Fₗ) →L[𝕜] Eₗ →L[𝕜] Gₗ

Apply L(x,-) pointwise to bilinear maps, as a continuous bilinear map

Defined in

Mathlib.Analysis.Normed.Operator.Bilinear

Cited by

17 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedAddCommGroupSeminormedAddCommGroupSeminormedAddCommGroupSeminormedAddCommGroupNontriviallyNormedFieldNormedSpaceNormedSpaceNormedSpaceNormedSpace