Commun. Korean Math. Soc. 2019; 34(2): 477-486
Online first article September 7, 2018 Printed April 30, 2019
https://doi.org/10.4134/CKMS.c180110
Copyright © The Korean Mathematical Society.
Seunghwan Baek, Mi Ryeong Lee
Kyungpook National University; Daegu Catholic University
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}.
Keywords: weighted shifts, hyponormality, semi-cubic hyponormality
MSC numbers: 47B37, 47B20
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