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Benchiheb, Otmane; Sadek, Fatimaezzahra; Amouch, Mohamed
Afrika matematika/Afrika mathematica, 03/2023, Letnik: 34, Številka: 1Journal Article
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 ∈ K and n ∈ N such that λ T n ( 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 also investigate the basic properties of these two notions. In addition, we discuss the spectrum of these two operators. At the end, we study the super-recurrence, the super-rigidity and the uniform super-rigidity behaviors on finite-dimensional spaces.
