2021/08/03 by Otmane Benchiheb, Benchiheb, Otmane, Fatimaezzahra Sadek +3
Decision Sciences · Mathematics · #37B20 #47A16 #Advanced Topics in Algebra #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Fuzzy and Soft Set Theory
paper · pdf · doi:10.48550/arxiv.2108.01424
openalex publication_date 2021/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An operator T acting on a Banach space X is said to be super-recurrent if for each open subset U of X, there exist λ∈\mathbbK and n∈ ℕ such that λTn(U)∩ U≠∅. In this paper, we introduce and study the notions of super-rigidity and uniform super-rigidity which are related to the notion of super-recurrence. We investigate some properties of these classes of operators and show that they share some properties with super-recurrent operators. At the end, we study the case of finite-dimensional spaces.