Weak and quadratic hyponormality of 2-variable weighted shifts and their examples
Bull. Korean Math. Soc. 2017 Vol. 54, No. 2, 633-646
Published online January 4, 2017
Printed March 31, 2017
Chunji Li
Northeastern University
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 $\left( W_{1},W_{2}\right) $. In addition, we detect the weak and quadratic hyponormality with some interesting 2-variable weighted shifts.
Keywords : weakly hyponormal, quadratically hyponormal, 2-variable weighted shifts
MSC numbers : Primary 47B37; Secondary 47B20
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