• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.477-486
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• 2019

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 ${\mathcal{U}}:=\{(x,y):W_{\alpha}$ is semi-cubically hyponormal} and describe the shape of the boundary of ${\mathcal{U}}$. In particular, we improve the results of [19, Theorem 4.2].