Topological transitive sequence of cosine operators on Orlicz space

Abstract

For a Young function $\varphi$ and a locally compact second countable group $G,$ let $L^{\varphi }(G)$ 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 $\{C_n{\}}_{n=1}^{\infty }:=\{\frac{1}{2}(T_{g,w}^n+S_{g,w}^n){\}}_{n=1}^{\infty }$, defined on $L^{\varphi }(G)$. 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.

11 pages, Typos corrected, Title changed