• Title, Summary, Keyword: hyponormal operators

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SPECTRAL CONTINUITY OF ESSENTIALLY p-HYPONORMAL OPERATORS

  • Kim, An-Hyun;Kwon, Eun-Young
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.2
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    • pp.389-393
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    • 2006
  • In this paper it is shown that the spectrum ${\sigma}$ is continuous at every p-hyponormal operator when restricted to the set of essentially p-hyponormal operators and moreover ${\sigma}$ is continuous when restricted to the set of compact perturbations of p-hyponormal operators whose spectral pictures have no holes associated with the index zero.

REMARKS ON SPECTRAL PROPERTIES OF p-HYPONORMAL AND LOG-HYPONORMAL OPERATORS

  • DUGGAL BHAGWATI P.;JEON, IN-HO
    • Bulletin of the Korean Mathematical Society
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    • v.42 no.3
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    • pp.543-554
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    • 2005
  • In this paper it is proved that for p-hyponormal or log-hyponormal operator A there exist an associated hyponormal operator T, a quasi-affinity X and an injection operator Y such that TX = XA and AY = YT. The operator A and T have the same spectral picture. We apply these results to give brief proofs of some well known spectral properties of p-hyponormal and log­hyponormal operators, amongst them that the spectrum is a con­tinuous function on these classes of operators.

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.

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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ON THE JOINT WEYL AND BROWDER SPECTRA OF HYPONORMAL OPERTORS

  • Lee, Young-Yoon
    • Communications of the Korean Mathematical Society
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    • v.16 no.2
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    • pp.235-241
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    • 2001
  • In this paper we study some properties of he joint Weyl and Browder spectra for the slightly larger classes containing doubly commuting n-tuples of hyponormal operators.

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SOME WEAK HYPONORMAL CLASSES OF WEIGHTED COMPOSITION OPERATORS

  • Jabbarzadeh, Mohammad R.;Azimi, Mohammad R.
    • Bulletin of the Korean Mathematical Society
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    • v.47 no.4
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    • pp.793-803
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    • 2010
  • In this note, we discuss measure theoretic characterizations for weighted composition operators in some operator classes on $L^2(\cal{F})$ such as, p-quasihyponormal, p-paranormal, p-hyponormal and weakly hyponormal. Some examples are then presented to illustrate that weighted composition operators lie between these classes.

THE HYPERINVARIANT SUBSPACE PROBLEM FOR QUASI-n-HYPONORMAL OPERATORS

  • Kim, An-Hyun;Kwon, Eun-Young
    • Communications of the Korean Mathematical Society
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    • v.22 no.3
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    • pp.383-389
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    • 2007
  • In this paper we examine the hyperinvariant subspace problem for quasi-n-hyponormal operators. The main result on this problem is as follows. If T = N + K is such that N is a quasi-n-hyponormal operator whose spectrum contains an exposed arc and K belongs to the Schatten p-ideal then T has a non-trivial hyperinvariant subspace.