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

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.1
• /
• pp.181-190
• /
• 2013

In this paper we study the Putinar's matricial model operator of rank 2 and provide some evidences for the validity of the conjecture in [8].

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

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.2
• /
• pp.633-646
• /
• 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.