• Korean Journal of Mathematics
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• v.17 no.3
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• pp.293-298
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• 2009

In this paper we make a connection between the specific class of weighted shifts and general study of k-hyponormality. We show how the k-hyponormality of an arbitrary operator can be ascertained by examining the k-hyponormality of an associated family of weighted shifts.

• 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.

• Journal of the Korean Mathematical Society
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• v.56 no.6
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• pp.1489-1502
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• 2019

This paper describes when a partial isometry satisfies several weak normal properties. Topics treated include quasi-normality, subnormality, hyponormality, p-hyponormality (p > 0), w-hyponormality, paranormality, normaloidity, spectraloidity, the von Neumann property and Weyl's theorem.

• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.1027-1041
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• 2008

In this paper we consider the hyponormality of Toeplitz operators $T_{\varphi}$ on the Bergman space $L_a^2{(\mathbb{D})$ in the cases, where ${\varphi}\;:=f+\bar{g}$ (f and g are polynomials). We present some necessary or sufficient conditions for the hyponormality of $T_{\varphi}$ under certain assumptions about the coefficients of ${\varphi}$.

• Korean Journal of Mathematics
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• v.15 no.2
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• pp.185-193
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• 2007

In this paper we consider the hyponormality of Toeplitz operators $T_{\varphi}$ on the Bergman space $L^2_a({\mathbb{D})$ with symbol in the case of function $f+{\overline{g}}$ with polynomials $f$ and $g$. We present some necessary conditions for the hyponormality of $T_{\varphi}$ under certain assumptions about the coefficients of ${\varphi}$.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.621-642
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• 2009

In this paper we give necessary and sufficient conditions that two Toeplitz operators with monomial symbols acting on the weighted Bergman space commute. We also present necessary and sufficient conditions for the hyponormality of Toeplitz operators with some special symbols on the weighted Bergman space. All the results are stated in terms of the Mellin transform of the symbol.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.15-24
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• 2022

Let p > 1 and α^[p](x) : $\sqrt{x}$, $\sqrt{\frac{p}{^2p-1}}$, $\sqrt{\frac{2p-1}{3p-2}}$, … , with 0 < x ≤ $\frac{p}{2p-1}$. In [10], the authors considered the subnormality, n-hyponormality and positive quadratic hyponormality of W_α^[p](x). By continuing to study, in this paper, we give a sufficient condition of quadratic hyponormality of W_α^[p](x). Finally, we give an example to characterize the gaps of W_α^[p](x) distinctively.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.65-73
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• 2011

In this note we present some necessary and sufficient conditions for the hyponormality of Toeplitz operators $T_{\varphi}$ under certain assumptions concerning the trigonometric polynomial symbol ${\varphi}$.

• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.73-83
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• 2019

In this article, we introduce a new kind of subnormal weighted shifts, which is a generalized form of Bergman shift, and discuss the k-hyponormality of its backward extensions.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.237-252
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• 2014

In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators $T_{\Phi}$, where ${\Phi}$ = $F+G^*$, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space $L^2_a(\mathbb{D},\mathbb{C}^n)$. We also show some necessary conditions for the hyponormality of $T_{F+G^*}$ with $F+G^*{\in}h^{\infty}{\otimes}M_{n{\times}n}$ on $L^2_a(\mathbb{D},\mathbb{C}^n)$.