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Cyclic behavior of the Cesàro operator on $L_2(0,\infty )$.
- Source :
-
Proceedings of the American Mathematical Society . Dec2008, Vol. 137 Issue 6, p2049-2055. 7p. - Publication Year :
- 2008
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 137
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 36596028