• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1471-1481
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• 2016

We characterize reducing subspaces of weighted shifts with operator weights as wandering invariant subspaces of the shifts with additional structures. We show how some earlier results on reducing subspaces of powers of weighted shifts with scalar weights on the unit disk and the polydisk can be fitted into our general framework.

• 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.51 no.2
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• pp.363-382
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• 2014

In this paper we first characterize the hereditarily hypercyclicity of the unilateral (or bilateral) weighted shifts on the spaces $L^2(\mathbb{N},\mathcal{K})$ (or $L^2(\mathbb{Z},\mathcal{K})$) with weight sequence {$A_n$} of positive invertible diagonal operators on a separable complex Hilbert space $\mathcal{K}$. Then we give the necessary and sufficient conditions for the supercyclicity of those weighted shifts, which extends some previous results of H. Salas. At last, we give some conditions for the supercyclicity of three different weighted shifts.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.123-135
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• 2016

In this article, we introduce the transforms of Pythagorean and quadratic means of weighted shifts. We then explore how the transforms of weighted shifts behaves, in comparison with the Aluthge transform.

• Kyungpook Mathematical Journal
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• v.45 no.3
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• pp.413-421
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• 2005

In this paper, we have a further discussion about quadratically hyponormal weighted shifts with weight sequence ${\alpha}:1,1,{\sqrt{a}},\left({\sqrt{b}},{\sqrt{c}},{\sqrt{d}}\right)^{\wedge}$ on the basis of sufficient conditions for positively quadratically hyponormal weighted shifts. We set examples of quadratically hyponormal weighted shifts with weight sequence of the above form, and also establish a general method for setting examples.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.99-103
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• 2014

In this paper, we characterize the m-isometric weighted shifts, using this characterization, we study the relations between the hyponormality and the m-isometricity of operators.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.579-590
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• 2020

The flatness property of a unilateral weighted shifts is important to study the gaps between subnormality and hyponormality. In this paper, we first summerize the results on the flatness for some special kinds of a weighted shifts. And then, we consider the flatness property for a local-cubically hyponormal weighted shifts, which was introduced in [2]. Let α : ${\sqrt{\frac{2}{3}}}$, ${\sqrt{\frac{2}{3}}}$, $\{{\sqrt{\frac{n+1}{n+2}}}\}^{\infty}_{n=2}$ and let W_α be the associated weighted shift. We prove that W_α is a local-cubically hyponormal weighted shift W_α of order ${\theta}={\frac{\pi}{4}}$ by numerical calculation.

• East Asian mathematical journal
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• v.31 no.5
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• pp.695-706
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• 2015

Let ${\mathcal{H}}$ be an infinite dimensional complex Hilbert space, and let $B({\mathcal{H}})$ be the algebra of all bounded linear operators on ${\mathcal{H}}$. Recall that an operator $T{\in}B({\mathcal{H})$ has property B(n) if ${\mid}T^n{\mid}{\geq}{\mid}T{\mid}^n$, $n{\geq}2$, which generalizes the class A-operator. We characterize the property B(n) of weighted shifts $S_{\lambda}$ over (${\eta},\;{\kappa}$)-type directed trees which appeared in the study of subnormality of weighted shifts over directed trees recently. In addition, we discuss the property B(n) of weighted shifts $S_{\lambda}$ over (2, 1)-type directed trees with nonzero weights are being distinct with respect to $n{\geq}2$. And we give some properties of weighted shifts $S_{\lambda}$ over (2, 1)-type directed trees with property B(2).

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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• pp.261-267
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• 2015

We study backward extensions of 2-variable weighted shifts with finite atomic Berger measure. We provide a necessary and sufficient condition for the subnormality of such extensions. As an application, we give a simple counterexample for the Curto-Muhly-Xia conjecture [10].