# On the Flatness of Semi-Cubically Hyponormal Weighted Shifts

Li, Chunji;Ahn, Ji-Hye

• Published : 2008.12.31
• 31 3

#### Abstract

Let $W_{\alpha}$ be a weighted shift with positive weight sequence ${\alpha}=\{\alpha_i\}_{i=0}^{\infty}$. The semi-cubical hyponormality of $W_{\alpha}$ is introduced and some flatness properties of $W_{\alpha}$ are discussed in this note. In particular, it is proved that if ${\alpha}_n={\alpha}_{n+1}$ for some $n{\geq}1$, ${{\alpha}_{n+k}}={\alpha}_n$ for all $k{\geq}1$.

#### Keywords

semi-cubically hyponormal;unilateral weighted shift;flatness

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#### Cited by

1. Flat phenomena of 2-variable weighted shifts vol.486, 2015, https://doi.org/10.1016/j.laa.2015.08.010