On recurrent sets of operators

Abstract

An operator $T$ acting on a Banach space $X$ is said to be recurrent if for each $U$; a nonempty open subset of $X$, there exists $n\in \mathbb{N}$ such that $T^n(U)\cap U\ne \varnothing .$ In the present work, we generalize this notion from a single operator to a set $\Gamma$ of operators. As application, we study the recurrence of $C$-regularized group of operators.

11 pages