2024/03/26 by Manuel Almeida Saavedra, Saavedra, Manuel, Manuel Stadlbauer +1
Mathematics · #37B20 #47A16 #Advanced Topics in Algebra #Approximation Theory and Sequence Spaces #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2403.17904
openalex publication_date 2024/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study recurrent operators from a new perspective by introducing the notion of hyper-recurrent operators and establish robust connections with quasi-rigid operators. For example, we prove that a recurrent operator on a separable Banach space is quasi-rigid if and only if it is a linear factor of a hyper-recurrent operator, and show that the quasi-rigid operators found in Costakis, Manoussos and Parissis's work, along with many others, are, in fact, hyper-recurrent operators. Furthermore, we provide a negative answer, using a class of operators introduced by Tapia, to the question by Costakis et al. whether T ⊕ T is recurrent whenever T is.