Theorems · Definition · functional analysis

ContinuousLinearMap.compL

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

Composition of continuous linear maps as a continuous bilinear map.

Defined in

Mathlib.Analysis.Normed.Operator.Bilinear

Cited by

27 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedAddCommGroupSeminormedAddCommGroupSeminormedAddCommGroupNontriviallyNormedFieldNormedSpaceNormedSpaceNormedSpace