Operator Ranges and Spaceability: Extending a Result of Kitson and Timoney
Abstract
We revisit the results of Kitson and Timoney [J.~Math.~Anal.~Appl.~378 (2011), 680--686] on the spaceability of complements of operator ranges, extending one of their main theorems to the general Fr\'echet setting. In particular, we provide an affirmative answer to the question posed in Remark~3.4 of that paper, showing that the conclusion remains valid when the operators act between Fr\'echet spaces. Moreover, we show that the same phenomenon occurs for arbitrary (possibly uncountable) families of operators. The arguments presented here follow the spirit of the original work.
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