Cyclic Behavior of the Cesàro Operator on L₂(0, ∞)

In this paper we study the cyclic properties of the infinite continuous Cesàro operator defined on L²(0, ∞) 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...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2009-06, Vol.137 (6), p.2049-2055
Main Authors: GONZALEZ, M, LEON-SAAVEDRA, F
Format: Article
Language:English
Subjects:
Banach space
Coefficients
Exact sciences and technology
General mathematics
General, history and biography
Hilbert spaces
Mathematical constants
Mathematical inequalities
Mathematical theorems
Mathematical vectors
Mathematics
Polynomials
Sciences and techniques of general use
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Summary:In this paper we study the cyclic properties of the infinite continuous Cesàro operator defined on L²(0, ∞) 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.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-09-09833-5