Cyclic behavior of the Cesàro operator on 𝐿₂(0,∞)

González, M.; León-Saavedra, F.

doi:10.1090/S0002-9939-09-09833-5

Cyclic behavior of the Cesàro operator on $L_2(0,\infty )$
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by M. González and F. León-Saavedra PDF

Proc. Amer. Math. Soc. 137 (2009), 2049-2055 Request permission

Abstract:

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.

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