Operator ranges and spaceability: An extension of the Kitson--Timoney theorem

In this paper we extend Theorem~3.3 from [\emph{J.~Math.~Anal.~Appl.}~\textbf{378} (2011), 680--686] concerning the spaceability of complements of operator ranges. In particular, we provide an affirmative answer to the question posed in \emph{Remark~3.4} of that paper, showing that the result remains valid when the operators act between Fréchet spaces. Moreover, we prove that the same conclusion holds for arbitrary (possibly uncountable) families of operators.