For a Young function $\phi$ and a locally compact second countable group $G,$ let $L^\phi(G)$ denote the Orlicz space on $G.$ In this article, we present a necessary and sufficient condition for the topological transitivity of a sequence of cosine operators $\{ C_n\}_{ n=1}^{ \infty}:=\{ \frac{ 1}{ 2}(T^n_{ g,w}+S^n_{ g,w})\}_{ n=1}^{ \infty}$, defined on $L^{ \phi}(G)$. We investigate the conditions for a sequence of cosine operators to be topological mixing. Moreover, we go on to prove the similar results for the direct sum of a sequence of the cosine operators. At the last, an example of a topological transitive sequence of cosine operators is given.
Categories: math.FA
