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A formula for $k$-hyponormality of backstep extensions of subnormal weighted shifts


Authors: Il Bong Jung and Chunji Li
Journal: Proc. Amer. Math. Soc. 129 (2001), 2343-2351
MSC (2000): Primary 47B37
DOI: https://doi.org/10.1090/S0002-9939-00-05844-5
Published electronically: December 28, 2000
MathSciNet review: 1823917
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Abstract:

Let ${\alpha }: {\alpha }_{0}, {\alpha }_{1}, \cdots $ be a weight sequence of positive real numbers and let $W_{{\alpha }}$ be a subnormal weighted shift with a weight sequence $\alpha $. Consider an extended weight sequence ${\alpha }(x) : x, {\alpha }_{0}, {\alpha }_{1}, \cdots $ with $0<x \le \alpha _{0}$and let $HE({\alpha ,k}):= \{ x >0: W_{\alpha (x)} \text{is} k \text{-hyponormal}\}$for $k \in {\mathbb{N}}\cup \{\infty \}$, where $\mathbb{N}$ is the set of natural numbers. We obtain a formula to find the interval $HE({\alpha ,k})\setminus HE({\alpha ,k+1})$, which provides several examples to distinguish the classes of $k$-hyponormal operators from one another.


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Additional Information

Il Bong Jung
Affiliation: Department of Mathematics, Kyungpook National University, Taegu 702–701, Korea
Email: ibjung@kyungpook.ac.kr

Chunji Li
Affiliation: Department of Mathematics, Yanbian University, Yanji 133-002, People’s Republic of China
Address at time of publication: TGRC, Kyungpook National University, Taegu 702-701, Korea
Email: chunjili@hanmail.com

DOI: https://doi.org/10.1090/S0002-9939-00-05844-5
Keywords: Subnormal weighted shifts, $k$-hyponormal weighted shifts
Received by editor(s): January 22, 1999
Received by editor(s) in revised form: December 7, 1999
Published electronically: December 28, 2000
Additional Notes: The first author was partially supported by KOSEF grant 971-0102-006-2 and the Korea Research Foundation made in the program year of 1998, 1998-015-D00019. The second author was partially supported by TGRC-KOSEF
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society