Topological transitive sequence of cosine operators on Orlicz space
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 September 2018
 arXiv:
 arXiv:1809.06085
 Bibcode:
 2018arXiv180906085A
 Keywords:

 Mathematics  Functional Analysis;
 47A16;
 46E30 (Primary) 22D05 (Secondary)
 EPrint:
 11 pages, Typos corrected, Title changed