Theorems · Theorem · functional analysis

IsBoundedLinearMap.isBigO_id

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} [inst : Semiring 𝕜] [inst_1 : SeminormedAddCommGroup E]
  [inst_2 : Module 𝕜 E] [inst_3 : SeminormedAddCommGroup F] [inst_4 : Module 𝕜 F] {f : E → F},
  IsBoundedLinearMap 𝕜 f → ∀ (l : Filter E), f =O[l] fun x => x

Defined in

Mathlib.Analysis.Normed.Operator.BoundedLinearMaps

Cited by

1 results in Mathlib

Foundations

Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSeminormedAddCommGroupModuleSeminormedAddCommGroupModule