Jumping flatness and Aluthge transform of recursive weighted shifts

TL;DR

This paper investigates the properties of Hamburger-type weighted shifts, focusing on the Aluthge transform and flatness concepts, providing new insights into subnormality and measure representation.

Contribution

It introduces the jumping flatness property for Hamburger-type weighted shifts and addresses the subnormality of their Aluthge transforms with finite support measures.

Findings

Affirmative answer to subnormality of Aluthge transform for finite support measures

Extension of flatness and jumping flatness notions for Hamburger-type shifts

Results on the representing measure of such weighted shifts

Abstract

We devote this paper to Hamburger type weighted shifts. We give in particular an affirmative answer to a problem concerning subnormality of the Aluthge transform of Hamburger moment measures with finite support. we also extend the notion flatness, jumping flatness property, introduced recently by Exner et all for Hamburger-type weighted shift and provide obtain several results related to the representing measure of such weighted shifts.