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

  • Li, Chunji (Department of Mathematics Northeastern University)
  • Received : 2016.03.17
  • Published : 2017.03.31

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.

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