Quasi-rigid operators and hyperrecurrence

We study recurrent operators from a new perspective by introducing the notion of hyperrecurrent 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 hyperrecurrent operator, and show that the quasi-rigid operators found in Costakis, Manoussos and Parissis’s work, along with many others, are, in fact, hyperrecurrent operators.