• Title/Summary/Keyword: quadratically hyponormal operators

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A PROPAGATION OF QUADRATICALLY HYPONORMAL WEIGHTED SHIFTS

  • Choi, Yong-Bin
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.347-352
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    • 2000
  • In this note we answer to a question of Curto: Non-first two equal weights in the weighted shift force subnormality in the presence of quadratic hyponormality. Also it is shown that every hyponormal weighted shift with two equal weights cannot be polynomially hyponormal without being flat.

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An Algorithm for Quartically Hyponormal Weighted Shifts

  • Baek, Seung-Hwan;Jung, Il-Bong;Moo, Gyung-Young
    • Kyungpook Mathematical Journal
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    • v.51 no.2
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    • pp.187-194
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    • 2011
  • 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.

The Flatness Property of Local-cubically Hyponormal Weighted Shifts

  • Baek, Seunghwan;Do, Hyunjin;Lee, Mi Ryeong;Li, Chunji
    • Kyungpook Mathematical Journal
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    • v.59 no.2
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    • pp.315-324
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    • 2019
  • In this note we introduce a local-cubically hyponormal weighted shift of order ${\theta}$ with $0{\leq}{\theta}{\leq}{\frac{\pi}{2}}$, which is a new notion between cubic hyponormality and quadratic hyponormality of operators. We discuss the property of flatness for local-cubically hyponormal weighted shifts.

WEAK AND QUADRATIC HYPONORMALITY OF 2-VARIABLE WEIGHTED SHIFTS AND THEIR EXAMPLES

  • Li, Chunji
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.2
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    • pp.633-646
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    • 2017
  • Recently, Curto, Lee and Yoon considered the properties (such as, hyponormality, subnormality, and flatness, etc.) for 2-variable weighted shifts and constructed several families of commuting pairs of subnormal operators such that each family can be used to answer a conjecture of Curto, Muhly and Xia negatively. In this paper, we consider the weak and quadratic hyponormality of 2-variable weighted shifts ($W_1,W_2$). In addition, we detect the weak and quadratic hyponormality with some interesting 2-variable weighted shifts.

SOME REMARKS ON THE HELTON CLASS OF AN OPERATOR

  • Kim, In-Sook;Kim, Yoen-Ha;Ko, Eun-Gil;Lee, Ji-Eun
    • Bulletin of the Korean Mathematical Society
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    • v.46 no.3
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    • pp.535-543
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    • 2009
  • In this paper we study some properties of the Helton class of an operator. In particular, we show that the Helton class preserves the quasinilpotent property and Dunford's boundedness condition (B). As corollaries, we get that the Helton class of some quadratically hyponormal operators or decomposable subnormal operators satisfies Dunford's boundedness condition (B).