In this paper, we provide the necessary and sufficient conditions under which a sequence of cosine operators is topologically multiply recurrent or recurrent on Orlicz spaces. Furthermore, we study several interesting special cases.

This paper characterizes the boundedness and compactness of the differences of weighted differentiation composition operators acting from the ?-Bloch space B? to the space H? of bounded holomorphic functions on the unit disk D.

In this article, we will discuss disjoint diskcyclicity for finitely many operators acting on a separable, infinite dimensional Fréchet space X . More precisely, we provide disjoint disk blow-up/collapse property and disjoint diskcyclicity criterion. In addition, we characterize the disjoint diskcyclicity for weighted shifts both in the bilateral and unilateral cases.

We characterize disjointness of supercyclic operators which map a holomorphic function to a partial sum of the Taylor expansion. In particular, we show that disjoint hypercyclicity equals disjoint supercyclicity for families of Taylor-type operators. Moreover, we give a sufficient condition to yield the disjoint supercyclicity for families of Taylor-type operators.