We study the notion of recurrence and some of its variations for linear operators acting on
Banach spaces. We characterize recurrence for several classes of linear operators such as …

In this paper, we introduce and study the notion of weak recurrence on a Banach space X. In
one hand, we prove some properties of this class of operators. On the other hand, we study …

Rigidity and non-recurrence along sequences Page 1 doi:10.1017/etds.2013.5 Rigidity and
non-recurrence along sequences V. BERGELSON†, A. DEL JUNCO‡, M. LEMA NCZYK§ …

We provide complete characterizations, on Banach spaces with cotype 2, of those linear
operators which happen to be weakly mixing or strongly mixing transformations with respect …

We study, for a continuous linear operator T on an F-space X, when the direct sum operator
T⊕ T is recurrent on X⊕ X. In particular: we establish the analogous notion, for recurrence …

Strong mixing Given two sets, over time the probability that points from one set end up in the
other set, converges to the product of the probabilities of the two sets. Weak mixing There …

The results of Bergelson, Host and Kra, and Leibman state that a multiple polynomial
correlation sequence can be decomposed into a sum of a nilsequence (a sequence defined …

Let $ T $ be a weakly almost periodic (WAP) linear operator on a Banach space $ X $. A
sequence of scalars $(a_n) _ {n\ge 1} ${\it modulates} $ T $ on $ Y\subset X $ if …

A technique is presented for multiplexing two ergodic measure preserving transformations
together to derive a third limiting transformation. This technique is used to settle a question …

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 …