Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On Semi-cubically Hyponormal Weighted Shifts with First Two Equal Weights

  • Received : 2016.02.24
  • Accepted : 2016.04.19
  • Published : 2016.09.23
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Abstract

It is known that a semi-cubically hyponormal weighted shift need not satisfy the 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 all semi-cubically hyponormal weighted shifts $W_{\alpha}$ with first two weights equal. Let ${\alpha}$ : 1, 1, ${\sqrt{x}}$(${\sqrt{u}}$, ${\sqrt{v}}$, ${\sqrt{w}}$)^ be a backward 3-step extension of a recursively generated weight sequence with 1 < x < u < v < w and let $W_{\alpha}$ be the associated weighted shift. In this paper we characterize completely the semi-cubical hyponormal $W_{\alpha}$ satisfying the additional assumption of the positive determinant coefficient property, which result is parallel to results for quadratic hyponormality.

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  1. Semi-cubic Hyponormality of Weighted Shifts with Stampfli Recursive Tail vol.88, pp.2, 2017, https://doi.org/10.1007/s00020-017-2373-y