Kyungpook Mathematical Journal

  • 제51권2호
  • /
  • Pages.187-194
  • /
  • 2011
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  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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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)
  • 투고 : 2010.12.30
  • 심사 : 2011.04.21
  • 발행 : 2011.06.30
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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.

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참고문헌

  1. R. Curto, Quadratically hyponormal weighted shifts, Integral Equations Operator Theory, 13(1990), 49-66. https://doi.org/10.1007/BF01195292
  2. R. Curto and L. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, Integral Equations Operator Theory, 17(1993), 202-246. https://doi.org/10.1007/BF01200218
  3. R. Curto and L. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, II, Integral Equations Operator Theory, 17(1993), 202-246. https://doi.org/10.1007/BF01200218
  4. R. Curto and I. B. Jung, Quadratically hyponormal weighted shifts with two equal weights, Integral Equations Operator Theory, 37(2000), 208-231. https://doi.org/10.1007/BF01192423
  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
  6. R. Curto and M. Putinar, Nearly subnormal operators and moment problems, J. Funct. Anal., 115(1993), 480-497. https://doi.org/10.1006/jfan.1993.1101
  7. G. Exner, I. B. Jung, and S. S. Park, Weakly n-hyponormal weighted shifts and their examples, Integral Equations Operator Theory, 54(2006), 215-233. https://doi.org/10.1007/s00020-004-1360-2
  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
  9. I. B. Jung and S. S. Park, Cubically hyponormal weighted shifts and their examples, J. Math. Anal. Appl., 247(2000), 557-569. https://doi.org/10.1006/jmaa.2000.6879
  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