Theorems · Definition · functional analysis

NormedSpace.induced

{F : Type u_6} →
  (𝕜 : Type u_7) →
    (E : Type u_8) →
      (G : Type u_9) →
        [inst : NormedField 𝕜] →
          [inst_1 : AddCommGroup E] →
            [inst_2 : Module 𝕜 E] →
              [inst_3 : SeminormedAddCommGroup G] →
                [inst_4 : NormedSpace 𝕜 G] →
                  [inst_5 : FunLike F E G] → [inst_6 : LinearMapClass F 𝕜 E G] → (f : F) → NormedSpace 𝕜 E

A linear map from a Module to a NormedSpace induces a NormedSpace structure on the domain, using the SeminormedAddCommGroup.induced norm. See note [reducible non-instances]

Defined in

Mathlib.Analysis.Normed.Module.Basic

Cited by

1 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedFieldAddCommGroupModuleSeminormedAddCommGroupNormedSpaceFunLikeLinearMapClass