Backward Aluthge Iterates of a Hyponormal Operator Have Scalar Extensions

The backward Aluthge iterate (defined below) of a hyponormal operator was initiated in [11]. In this paper we characterize the backward Aluthge iterate of a weighted shift. Also we show that the backward Aluthge iterate of a hyponormal operator has an analogue of the single valued extension property for . Finally, we show that backward Aluthge iterates of a hyponormal operator have scalar extensions. As a corollary, we get that the backward Aluthge iterate of a hyponormal operator has a nontrivial invariant subspace if its spectrum has interior in the plane.