Theorems · Theorem · functional analysis

IsBoundedLinearMap.isBigO_comp

∀ {𝕜 : Type u_1} {F : Type u_3} {G : Type u_4} [inst : Semiring 𝕜] [inst_1 : SeminormedAddCommGroup F]
  [inst_2 : Module 𝕜 F] [inst_3 : SeminormedAddCommGroup G] [inst_4 : Module 𝕜 G] {E : Type u_5} {g : F → G},
  IsBoundedLinearMap 𝕜 g → ∀ {f : E → F} (l : Filter E), (fun x' => g (f x')) =O[l] f

Defined in

Mathlib.Analysis.Normed.Operator.BoundedLinearMaps

Cited by

1 results in Mathlib

Foundations

Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSeminormedAddCommGroupModuleSeminormedAddCommGroupModule