Cyclic behavior of the Cesàro operator on $L_2(0,\infty )$.

In this paper we study the cyclic properties of the infinite continuous Cesàro operator defined on $L^2(0,infty )$ by $(C_infty f)(x)=frac {1}{x}int _0^x f(s) ds $. Despite this operator being cyclic, we show that it is not supercyclic; even more, it is not weakly supercyclic. These results complement some recent ones on the cyclic behavior of Cesàro operators. [ABSTRACT FROM AUTHOR]