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Orbits of Cesaro type operators

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León Saavedra, F. and Piqueras Lerena, A. and Seoane-Sepúlveda, Juan B. (2009) Orbits of Cesaro type operators. Mathematische Nachrichten, 282 (5). pp. 764-773. ISSN 0025-584X

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Official URL: http://onlinelibrary.wiley.com/doi/10.1002/mana.200610769/pdf


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Abstract

A bounded linear operator T on a Banach space X is called hypercyclic if there exists a vector x is an element of X such that its orbit, {T(n)x}, is dense in X. In this paper we show hypercyclic properties of the orbits of the Cesaro operator defined on different spaces. For instance, we show that the Cesaro operator defined on L(p)[0, 1] (1 < p < infinity) is hypercyclic. Moreover, it is chaotic and it has supercyclic subspaces. On the other hand, the Cesaro operator defined on other spaces of functions behave differently. Motivated by this, we study weighted Cesaro operators and different degrees of hypercyclicity are obtained. The proofs are based on the classical Muntz-Szasz theorem. We also propose problems and give new directions.


Item Type:Article
Uncontrolled Keywords:Hypercyclicity; supercyclicity; Cesaro operators; Hypercyclic subspaces
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:20033
Deposited On:21 Feb 2013 15:26
Last Modified:28 Nov 2016 08:23

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