Jumping flatness and Aluthge transform of recursive weighted shifts

Abstract

We devote this paper to Hamburger-type weighted shifts. We give first an affirmative answer to a problem concerning subnormality of the Aluthge transform of Hamburger moment measures with finite support. We also extend the notion of “the jumping flatness property” introduced recently in [11] for Hamburger-type weighted shifts and provide several results related to the representing measure of such weighted shifts.