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Aluthge transforms of unbounded weighted composition operators in L2-spaces |
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| Authors: | Chafiq Benhida Piotr Budzyński Jacek Trepkowski |
| Institution: | 1. Laboratoire Paul Painlevé, Université de Lille, Villeneuve d'Ascq, 59655 France;2. Katedra Zastosowań Matematyki, Uniwersytet Rolniczy w Krakowie, ul. Balicka 253c, Kraków, 30-198 Poland;3. Instytut Matematyki, Uniwersytet Jagielloński, ul. Łojasiewicza 6, Kraków, 30-348 Poland |
| Abstract: | We describe the Aluthge transform of an unbounded weighted composition operator acting in an L2-space. We show that its closure is also a weighted composition operator with the same symbol and a modified weight function. We investigate its dense definiteness. We characterize p-hyponormality of unbounded weighted composition operators and provide results on how it is affected by the Aluthge transformation. We show that the only fixed points of the Aluthge transformation on weighted composition operators are quasinormal ones. |
| Keywords: | Aluthge transform hyponormal operator weighted composition operator |