Theorems · Definition · functional analysis

ContinuousLinearMap.apply

(𝕜 : Type u_1) →
  {E : Type u_4} →
    (Fₗ : Type u_7) →
      [inst : SeminormedAddCommGroup E] →
        [inst_1 : SeminormedAddCommGroup Fₗ] →
          [inst_2 : NontriviallyNormedField 𝕜] →
            [inst_3 : NormedSpace 𝕜 E] → [inst_4 : NormedSpace 𝕜 Fₗ] → E →L[𝕜] (E →L[𝕜] Fₗ) →L[𝕜] Fₗ

The continuous semilinear map obtained by applying a continuous semilinear map at a given vector. This is the continuous version of LinearMap.applyₗ.

Defined in

Mathlib.Analysis.Normed.Operator.Bilinear

Cited by

23 results in Mathlib

Foundations

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

Assumes

SeminormedAddCommGroupSeminormedAddCommGroupNontriviallyNormedFieldNormedSpaceNormedSpace