Theorems · Theorem · functional analysis

IsLinearMap.with_bound

∀ {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},
  IsLinearMap 𝕜 f → ∀ (M : ℝ), (∀ (x : E), ‖f x‖ ≤ M * ‖x‖) → IsBoundedLinearMap 𝕜 f

Defined in

Mathlib.Analysis.Normed.Operator.BoundedLinearMaps

Cited by

7 results in Mathlib

Foundations

Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSeminormedAddCommGroupModuleSeminormedAddCommGroupModule