In this article, we address a problem posed by Bayart regarding the existence of an infinite‐dimensional closed vector subspace (excluding the null operator) within the set of supercyclic operators on Banach spaces. We fully resolve this problem by establishing the existence of the closed subspace. Furthermore, we prove that the set of supercyclic operators on contains, up to the null operator, an isometric copy of .
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Alves et al. (2024) studied this question.
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