Topological transitivity for cosine operators on Orlicz spaces

Vishvesh Kumar, Ibrahim Akbarbaglu, Mohammad Reza Azimi

Published 2018-09-17Version 1

For a Young function $\phi$ and a locally compact 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 the cosine operators $C_n:=\frac{1}{2}(T^n_{g,w}+S^n_{g,w})$ defined on $L^{\phi}(G)$. We investigate the conditions for the 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 operator. At the last, an example of a topological transitive cosine operator is given.