Theorems · Theorem · functional analysis

ContinuousAlternatingMap.norm_compContinuousLinearMap_le

∀ {𝕜 : Type u} {E : Type wE} {F : Type wF} {G : Type wG} {ι : Type v} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : SeminormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : SeminormedAddCommGroup F]
  [inst_4 : NormedSpace 𝕜 F] [inst_5 : SeminormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] [inst_7 : Fintype ι]
  (f : F [⋀^ι]→L[𝕜] G) (g : E →L[𝕜] F), ‖f.compContinuousLinearMap g‖ ≤ ‖f‖ * ‖g‖ ^ Fintype.card ι

Defined in

Mathlib.Analysis.Normed.Module.Alternating.Basic

Cited by

0 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpaceSeminormedAddCommGroupNormedSpaceFintype