Semi-cubically hyponormal weighted shifts with Stampfi's subnormal completion

TL;DR

This paper investigates the properties of semi-cubically hyponormal weighted shifts with Stampfli's subnormal completion, focusing on the region where these operators exhibit semi-cubic hyponormality and analyzing its boundary shape.

Contribution

It characterizes the region of semi-cubic hyponormality for weighted shifts with Stampfli's completion and refines previous results on its boundary properties.

Findings

Description of the region  where the weighted shift is semi-cubically hyponormal

Shape analysis of the boundary of 

Improved characterization compared to prior work

Abstract

Let $\alpha :1,(1,\sqrt{x},\sqrt{y})^{\wedge }$ be a weight sequence with Stampfli's subnormal completion and let $W_{\alpha }$ be its associated weighted shift. In this paper we discuss some properties of the region $\mathcal{U}:\mathcal{=}\{(x,y):W_{\alpha }$ is semi-cubically hyponormal$\}$ and describe the shape of the boundary of $\mathcal{U}$. In particular, we improve the results of \cite[Theorem 4.2]{LLB} with properties of $\mathcal{U}$.