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 λT 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 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.

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