Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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An Algorithm for Quartically Hyponormal Weighted Shifts

  • Baek, Seung-Hwan (Department of Mathematics, Kyungpook National University) ;
  • Jung, Il-Bong (Department of Mathematics, Kyungpook National University) ;
  • Moo, Gyung-Young (Department of Mathematics, Kyungpook National University)
  • Received : 2010.12.30
  • Accepted : 2011.04.21
  • Published : 2011.06.30
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Abstract

Examples of a quartically hyponormal weighted shift which is not 3-hyponormal are discussed in this note. In [7] Exner-Jung-Park proved that if ${\alpha}$(x) : $\sqrt{x},\sqrt{\frac{2}{3}},\sqrt{\frac{3}{4}},\sqrt{\frac{4}{5}},{\cdots}$ with 0 < x ${\leq}\;\frac{53252}{100000}$, then $W_{\alpha(x)}$ is quartically hyponormal but not 4-hyponormal. And, Curto-Lee([5]) improved their result such as that if ${\alpha}(x)$ : $\sqrt{x},\sqrt{\frac{2}{3}},\sqrt{\frac{3}{4}},\sqrt{\frac{4}{5}},{\cdots}$ with 0 < x ${\leq}\;\frac{667}{990}$, then $W_{\alpha(x)}$ is quartically hyponormal but not 3-hyponormal. In this note, we improve slightly Curto-Lee's extremal value by using an algorithm and computer software tool.

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References

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Cited by

  1. Backward Extensions of Recursively Generated Weighted Shifts and Quadratic Hyponormality vol.79, pp.1, 2014, https://doi.org/10.1007/s00020-014-2126-0
  2. Quadratically hyponormal weighted shifts with recursive tail vol.408, pp.1, 2013, https://doi.org/10.1016/j.jmaa.2013.05.058