Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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BACKWARD EXTENSIONS OF BERGMAN-TYPE WEIGHTED SHIFT

  • Li, Chunji (Department of Mathematics Northeastern University) ;
  • Qi, Wentao (Department of Mathematics Northeastern University) ;
  • Wang, Haiwen (Department of Mathematics Northeastern University)
  • Received : 2019.01.17
  • Accepted : 2019.06.26
  • Published : 2020.01.31
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Abstract

Let m ∈ ℕ0, p > 1 and $${\alpha}^{[m,p]}(x)\;:\;{\sqrt{x}},\;\{{\sqrt{\frac{(m+n-1)p-(m+n-2)}{(m+n)p-(m+n-1)}}}\}^{\infty}_{n=1}$$. In this paper, we consider the backward extensions of Bergman-type weighted shift Wα[m,p](x). We consider its subnormality, k-hyponormality and positive quadratic hyponormality. Our results include all the results on Bergman weighted shift Wα(x) with m ∈ ℕ and $${\alpha}(x)\;:\;{\sqrt{x}},\;{\sqrt{\frac{m}{m+1}},\;{\sqrt{\frac{m}{m+2}},\;{\sqrt{\frac{m+2}{m+3}},{\cdots}$$.

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