Topologically transitive sequence of cosine operators on Orlicz spaces
Tóm tắt
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 paper, 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 topologically mixing. Further, we go on to prove a similar result for the direct sum of a sequence of cosine operators. Finally, we give an example of topologically transitive sequence of cosine operators.
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