Weak and Quadratic Hyponormality of 2-Variable Weighted Shifts and Their Examples

Abstract

Abstract. 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.