DOI QR코드

DOI QR Code

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)
  • 투고 : 2010.12.30
  • 심사 : 2011.04.21
  • 발행 : 2011.06.30

초록

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.

키워드

참고문헌

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  5. R. Curto and S. H. Lee, Quartically hyponormal weighted shifts need not be 3- hyponormal, J. Math. Anal. Appl., 314(2006), 455-463. https://doi.org/10.1016/j.jmaa.2005.04.020
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  8. I. B. Jung and S. S. Park, Quadratically hyponormal weighted shifts and their exam- ples, Integral Equations Operator Theory, 36(2000), 480-498. https://doi.org/10.1007/BF01232741
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  10. Wolfram Research, Inc., Mathematica, Version 8.0, Wolfram Research Inc., Cham- paign, IL, 2010.

피인용 문헌

  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