WEAK AND QUADRATIC HYPONORMALITY OF 2-VARIABLE WEIGHTED SHIFTS AND THEIR EXAMPLES

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 $\left( W_{1},W_{2}\right) $. In addition, we detect the weak and quadratic hyponormality with some interesting 2-variable weighted shifts. KCI Citation Count: 0