Semi-cubic hyponormality of weighted shifts with stampfli recursive tail

TL;DR

This paper characterizes the semi-cubic hyponormality of certain weighted shift operators with recursive tail structures, providing conditions and examples for this property in operator theory.

Contribution

It introduces a characterization of semi-cubic hyponormality for weighted shifts with Stampfli recursive tails, expanding understanding of hyponormality conditions.

Findings

Characterization of semi-cubic hyponormality for specific weighted shifts.

Identification of conditions involving recursive tail structures.

Examples illustrating the theoretical results.

Abstract

Let $\alpha :\sqrt{x_{m}},\cdots ,\sqrt{x_{1}},(\sqrt{u},\sqrt{v},\sqrt{w}% )^{\wedge}$ be a backward $m$-step extension of a recursive weight sequence and let $% W_{\alpha }$ be the weighted shift associated with $\alpha $. In this paper we characterize the semi-cubic hyponormality of $W_{\alpha }$ having the positive determinant coefficient property and discuss some related examples.