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The role of the angle in supercyclic behavior

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Gallardo Gutiérrez, Eva A. and Montes Rodríguez, Alfonso (2003) The role of the angle in supercyclic behavior. Journal of Functional Analysis, 203 (1). pp. 27-43. ISSN 0022-1236

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022123602000423


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Abstract

A bounded operator T acting on a Hilbert space H is said to be supercyclic if there is a vector f epsilon H such that the projective orbit {lambdaT(n)f: ngreater than or equal to0 and lambda epsilon C} is dense in H. We use a new method based on a very simple geometric idea that allows us to decide whether an operator is supercyclic or not. The method is applied to obtain the following result: A composition operator acting on the Hardy space whose inducing symbol is a parabolic linear-fractional map of the disk onto a proper subdisk is not supercyclic. This result finishes the characterization of the supercyclic behavior of composition operators induced by linear fractional maps and, thus, completes previous work of Bourdon and Shapiro.


Item Type:Article
Uncontrolled Keywords:Cyclic operators; Supercyclic operators; Composition operator; Hardy space; Inner functions; Gerschgorin's Theorem
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:21116
Deposited On:26 Apr 2013 10:34
Last Modified:10 Aug 2018 11:37

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