• Korean Journal of Mathematics
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• v.23 no.1
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• pp.199-203
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• 2015

In this paper we give an example which is a weakly subnormal weighted shift but not 2-hyponormal. Also, we show that every partially normal extension of an isometry T needs not be 2-hyponormal even though p.n.e.(T) is weakly subnormal.

• Honam Mathematical Journal
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• v.39 no.1
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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.

• 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.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.683-689
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• 2009

We investigate the gaps among classes of weakly hyponormal composition operators induced by Embry characterization for the subnormality. The relationship between subnormality and weak hyponormality will be discussed in a version of composition operator induced by a non-singular measurable transformation.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.287-292
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• 2008

We introduce jointly weak subnormal operators. It is shown that if $T=(T_1,T_2)$ is subnormal then T is weakly subnormal and if f $T=(T_1,T_2)$ is weakly subnormal then T is hyponormal. We discuss the flatness of weak subnormal operators.

• 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.