∀ {M₁ : Type u_3} {M₂ : Type u_4} [inst : TopologicalSpace M₁] [inst_1 : AddCommMonoid M₁]
  [inst_2 : TopologicalSpace M₂] [inst_3 : AddCommMonoid M₂] {S : Type u_6} [inst_4 : Monoid S]
  [inst_5 : DistribMulAction S M₂] [ContinuousConstSMul S M₂] {f : M₁ → M₂} {c : S},
  IsUnit c → (IsCompactOperator (c • f) ↔ IsCompactOperator f)