East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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SOME INEQUALITIES OF WEIGHTED SHIFTS ASSOCIATED BY DIRECTED TREES WITH ONE BRANCHING POINT

  • KIM, BO GEON (DEPARTMENT OF MATHEMATICS, KYUNGPOOK NATIONAL UNIVERSITY) ;
  • SEO, MINJUNG (DEPARTMENT OF MATHEMATICS, KYUNGPOOK NATIONAL UNIVERSITY)
  • Received : 2015.07.06
  • Accepted : 2015.09.14
  • Published : 2015.09.30
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Abstract

Let ${\mathcal{H}}$ be an infinite dimensional complex Hilbert space, and let $B({\mathcal{H}})$ be the algebra of all bounded linear operators on ${\mathcal{H}}$. Recall that an operator $T{\in}B({\mathcal{H})$ has property B(n) if ${\mid}T^n{\mid}{\geq}{\mid}T{\mid}^n$, $n{\geq}2$, which generalizes the class A-operator. We characterize the property B(n) of weighted shifts $S_{\lambda}$ over (${\eta},\;{\kappa}$)-type directed trees which appeared in the study of subnormality of weighted shifts over directed trees recently. In addition, we discuss the property B(n) of weighted shifts $S_{\lambda}$ over (2, 1)-type directed trees with nonzero weights are being distinct with respect to $n{\geq}2$. And we give some properties of weighted shifts $S_{\lambda}$ over (2, 1)-type directed trees with property B(2).

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References

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