On the set of supercyclic operators

2024/03/27 by Alves, Thiago R., Souza, Gustavo C.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2403.18678

Abstract

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 ℓ₁ contains, up to the null operator, an isometric copy of ℓ₁.

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