  In this article, we address a problem posed by F. 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 resolve
this problem by establishing the existence of the closed subspace. Furthermore,
we prove that the set of supercyclic operators on $\ell_1$ contains, up to the
null operator, an isometric copy of $\ell_1$.
