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http://dx.doi.org/10.14317/jami.2020.579

WHICH WEIGHTED SHIFTS ARE FLAT ?  

SHEN, HAILONG (Department of Mathematics, Northeastern University)
LI, CHUNJI (Department of Mathematics, Northeastern University)
Publication Information
Journal of applied mathematics & informatics / v.38, no.5_6, 2020 , pp. 579-590 More about this Journal
Abstract
The flatness property of a unilateral weighted shifts is important to study the gaps between subnormality and hyponormality. In this paper, we first summerize the results on the flatness for some special kinds of a weighted shifts. And then, we consider the flatness property for a local-cubically hyponormal weighted shifts, which was introduced in [2]. Let α : ${\sqrt{\frac{2}{3}}}$, ${\sqrt{\frac{2}{3}}}$, $\{{\sqrt{\frac{n+1}{n+2}}}\}^{\infty}_{n=2}$ and let Wα be the associated weighted shift. We prove that Wα is a local-cubically hyponormal weighted shift Wα of order ${\theta}={\frac{\pi}{4}}$ by numerical calculation.
Keywords
quadratically hyponormal; cubically hyponormal; weighted shifts;
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Times Cited By KSCI : 5  (Citation Analysis)
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