• Kyungpook Mathematical Journal
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• 제51권2호
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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.

• 대한수학회보
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• 제42권2호
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• pp.269-277
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• 2005

The tensor product $A{\bigotimes}B$ of Hilbert space operators A and B will be shown to be log-hyponormal if and only if A and Bare log-hyponormal. Some general comments about generalized hyponormality are also made.

• 호남수학학술지
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• 제39권1호
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• pp.83-91
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• 2017

In this note we consider weakly hyponormal weighted shift. In particular, we focus on the weak 4-hyponormality of the weighted shift with the Bergman tail. This is related to the open question of finding a polynomially hyponormal non-subnormal weighted shift.

• 대한수학회보
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• 제43권2호
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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.

• 대한수학회보
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• 제37권2호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권3호
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• pp.161-167
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• 2005

In this note we consider the projective property $\sigma(Re(T))\;=\;Re\;(\sigma$(T))$ of p-hyponormal operators and log-hyponormal operators.

• 대한수학회논문집
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• 제16권2호
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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.

• 대한수학회보
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• 제51권4호
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• pp.1031-1040
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• 2014

In this paper, we show that any cubically hyponormal weighted shift with first two equal weights is flat. And we give an example of a weighted shift which is not cubically hyponormal but almost-cubically hyponormal.

• 대한수학회지
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• 제53권1호
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• pp.233-246
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• 2016

In this paper, we introduce the class of analytic extensions of M-hyponormal operators and we study various properties of this class. We also use a special Sobolev space to show that every analytic extension of an M-hyponormal operator T is subscalar of order 2k + 2. Finally we obtain that an analytic extension of an M-hyponormal operator satisfies Weyl's theorem.

• 대한수학회논문집
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• 제13권1호
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• pp.21-27
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• 1998

In this paper we prove a structure theorem for p-hyponomal contractions and also give an example of a p-hyponormal operator which is not *-paranormal.