Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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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.

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

Seunghwan Baek, Mi Ryeong Lee

Kyungpook National University; Daegu Catholic University

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}.

Keywords: weighted shifts, hyponormality, semi-cubic hyponormality

MSC numbers: 47B37, 47B20

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