The role of the angle in supercyclic behavior |
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Authors: | Eva A Gallardo-Gutiérrez |
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Institution: | a Departamento de Matemáticas, Universidad de Cádiz, Apartado 40, Puerto Real (Cádiz) 11510, Spain b Departamento de Análisis Matemático, Facultad de Matemáticas, Avenida Reina Mercedes, Apartado 1160, Sevilla 41080, Spain |
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Abstract: | A bounded operator T acting on a Hilbert space is said to be supercyclic if there is a vector such that the projective orbit and is dense in . 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. |
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Keywords: | primary 47A16 47B33 47B38 |
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