An Algorithm for Quartically Hyponormal Weighted Shifts

• Journal title : Kyungpook mathematical journal
• Volume 51, Issue 2,  2011, pp.187-194
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2011.51.2.187
Title & Authors
An Algorithm for Quartically Hyponormal Weighted Shifts
Baek, Seung-Hwan; Jung, Il-Bong; Moo, Gyung-Young;

Abstract
Examples of a quartically hyponormal weighted shift which is not 3-hyponormal are discussed in this note. In [7] Exner-Jung-Park proved that if $\small{{\alpha}}$(x) : $\small{\sqrt{x},\sqrt{\frac{2}{3}},\sqrt{\frac{3}{4}},\sqrt{\frac{4}{5}},{\cdots}}$ with 0 < x $\small{{\leq}\;\frac{53252}{100000}}$, then $\small{W_{\alpha(x)}}$ is quartically hyponormal but not 4-hyponormal. And, Curto-Lee([5]) improved their result such as that if $\small{{\alpha}(x)}$ : $\small{\sqrt{x},\sqrt{\frac{2}{3}},\sqrt{\frac{3}{4}},\sqrt{\frac{4}{5}},{\cdots}}$ with 0 < x $\small{{\leq}\;\frac{667}{990}}$, then $\small{W_{\alpha(x)}}$ is quartically hyponormal but not 3-hyponormal. In this note, we improve slightly Curto-Lee`s extremal value by using an algorithm and computer software tool.
Keywords
quartically hyponormal operators;cubically hyponormal operators;quadratically hyponormal operators;weighted shifts;
Language
English
Cited by
1.
Backward Extensions of Recursively Generated Weighted Shifts and Quadratic Hyponormality, Integral Equations and Operator Theory, 2014, 79, 1, 49
2.
Quadratically hyponormal weighted shifts with recursive tail, Journal of Mathematical Analysis and Applications, 2013, 408, 1, 298
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