Semi-cubic hyponormality of weighted shifts with stampfli recursive tail

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

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