Aluthge transforms of unbounded weighted composition operators in L2‐spaces

Chafiq Benhida, Piotr Budzyński and Jacek Trepkowski

Mathematische Nachrichten, 2020, vol. 293, issue 10, 1888-1910

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.

Date: 2020
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