Abstract
In this note we study the k-hyponormality and the subnormality of Aluthge transforms of weighted shifts. It is shown that Aluthge transforms of weighted shifts need not preserve the k-hyponormality. Moreover, we show that if Wα is a subnormal weighted shift with 2-atomic Berger measure then its Aluthge transform \({\widetilde{W}_\alpha}\) is subnormal if and only if at least one of two atoms is zero.
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