sub — Mathlib

English

If f is a compact operator and V is a closed subspace with certain containment, then restricting f to V via codRestrict yields a compact operator.

Русский

Если f компактный оператор и V — замкнутое подпространство, то ограничение codRestrict сохраняет компактность.

LaTeX

$$$IsCompactOperator(f) \Rightarrow IsCompactOperator(Set.codRestrict(f, V, hV))$, under hV and closedness$$

Lean4

theorem sub [IsTopologicalAddGroup M₄] {f g : M₁ → M₄} (hf : IsCompactOperator f) (hg : IsCompactOperator g) :
    IsCompactOperator (f - g) := by rw [sub_eq_add_neg]; exact hf.add hg.neg

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