neg — Mathlib

English

If f is a compact operator and V is a subspace closed under the ambient structure, then the restriction of f to V is compact.

Русский

Если f компактный оператор и V — подпространство, то ограничение f на V компактно.

LaTeX

$$$IsCompactOperator(f) \Rightarrow IsCompactOperator(f|_V)$, under suitable closedness of V$$

Lean4

theorem neg [ContinuousNeg M₄] {f : M₁ → M₄} (hf : IsCompactOperator f) : IsCompactOperator (-f) :=
  let ⟨K, hK, hKf⟩ := hf
  ⟨-K, hK.neg, mem_of_superset hKf fun x (hx : f x ∈ K) => Set.neg_mem_neg.mpr hx⟩

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