Theorems · Definition · functional analysis

SchwartzMap.postcompCLM

{𝕜 : Type u_2} →
  {E : Type u_5} →
    {F : Type u_6} →
      {G : Type u_7} →
        [inst : NormedAddCommGroup E] →
          [inst_1 : NormedSpace ℝ E] →
            [inst_2 : NormedAddCommGroup F] →
              [inst_3 : NormedSpace ℝ F] →
                [inst_4 : RCLike 𝕜] →
                  [inst_5 : NormedSpace 𝕜 F] →
                    [inst_6 : NormedAddCommGroup G] →
                      [inst_7 : NormedSpace ℝ G] →
                        [inst_8 : NormedSpace 𝕜 G] → (F →L[𝕜] G) → SchwartzMap E F →L[𝕜] SchwartzMap E G

Postcomposition with a continuous linear map is a continuous linear map on Schwartz functions.

Defined in

Mathlib.Analysis.Distribution.SchwartzSpace.Basic

Cited by

2 results in Mathlib

Foundations

Depth 225 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceRCLikeNormedSpaceNormedAddCommGroupNormedSpaceNormedSpace