On Semi-cubically Hyponormal Weighted Shifts with First Two Equal Weights
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It is known that a semi-cubically hyponormal weighted shift need not satisfythe flatness property, in which equality of two weights forces all or almost all weights to be equal. So it is a natural question to describe allsemi-cubically hyponormal weighted shifts $W_{\alpha }$ with first two weights equal. Let $\alpha :1,1,\sqrt{x},(\sqrt{u},\sqrt{v},\sqrt{w})^{\wedge }$be a backward 3-step extension of a recursively generated weight sequencewith $1<x<u<v<w$ and let $W_{\alpha }$ be the associated weighted shift. In this paper we characterize completely thesemi-cubical hyponormal $W_{\alpha }$ satisfying the additional assumption of thepositive determinantcoefficient property, which result is parallel to results for quadratichyponormality.
Abstract
It is known that a semi-cubically hyponormal weighted shift need not satisfythe flatness property, in which equality of two weights forces all or almost all weights to be equal. So it is a natural question to describe allsemi-cubically hyponormal weighted shifts $W_{\alpha }$ with first two weights equal. Let $\alpha :1,1,\sqrt{x},(\sqrt{u},\sqrt{v},\sqrt{w})^{\wedge }$be a backward 3-step extension of a recursively generated weight sequencewith $1<x<u<v<w$ and let $W_{\alpha }$ be the associated weighted shift. In this paper we characterize completely thesemi-cubical hyponormal $W_{\alpha }$ satisfying the additional assumption of thepositive determinantcoefficient property, which result is parallel to results for quadratichyponormality.
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