instContinuousConstSMul — Mathlib

English

A variant of von Neumann boundedness: IsVonNBounded R S holds iff the image under f of points in S is bounded in a canonical sense for the operator space.

Русский

Альтернативное определение von Neumann ограниченности: IsVonNBounded R S эквивалентно тому, что отображение через элементы S ограничивает образ точек.

LaTeX

$$$$ IsVonNBounded_R(S) \iff \forall x \in S, \text{...} $$$$

Lean4

instance instContinuousConstSMul (M : Type*) [Monoid M] [DistribMulAction M F] [SMulCommClass 𝕜₂ M F]
    [TopologicalSpace F] [IsTopologicalAddGroup F] [ContinuousConstSMul M F] (𝔖 : Set (Set E)) :
    ContinuousConstSMul M (UniformConvergenceCLM σ F 𝔖) :=
  let _ := IsTopologicalAddGroup.toUniformSpace F
  have _ : IsUniformAddGroup F := isUniformAddGroup_of_addCommGroup
  have _ := uniformContinuousConstSMul_of_continuousConstSMul M F
  inferInstance

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