Theorems · Definition · functional analysis

ContinuousLinearMap.smulRightL

(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] → StrongDual 𝕜 E →L[𝕜] Fₗ →L[𝕜] E →L[𝕜] Fₗ

ContinuousLinearMap.smulRight as a continuous trilinear map: smulRightL (c : StrongDual 𝕜 E) (f : F) (x : E) = c x • f. This is also known as a rank-one operator. See also InnerProductSpace.rankOne for the rank-one operator on Hilbert spaces.

Defined in

Mathlib.Analysis.Normed.Operator.Bilinear

Cited by

15 results in Mathlib

Foundations

Depth 176 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SeminormedAddCommGroupSeminormedAddCommGroupNontriviallyNormedFieldNormedSpaceNormedSpace